Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
Find the quotient: (x411x27x6)(x+3) .Find the quotient: (x264)(x4) .Find the quotient: (125x38)(5x2) .Use synthetic division to find the quotient and remainder when 3x3+10x2+6x2 is divided by x+2 .Use synthetic division to find the quotient and remainder when 4x3+5x25x+3 is divided by x+2 .Use synthetic division to find the quotient and remainder when x416x2+5x+20 is divided by x+4 .Use synthetic division to find the quotient and remainder when x49x2+2x+6 is divided by x+3 .For functions f(x)=x25x24 and g(x)=x+3 , find (a) (fg)(x) (b) (fg)(3) .For functions f(x)=x25x36 and g(x)=x+4 , find (a) (fg)(x) (b) (fg)(5) .Use the Remainder Theorem to find the remainder when f(x)=x3+4x+15 is divided by x+2 .Use the Remainder Theorem to find the remainder when f(x)=x37x+12 is divided by x+3 .Use the Factor Theorem to determine if x5 is a factor of f(x)=x3125 .Use the Factor Theorem to determine if x6 is a factor of f(x)=x3216 .In the following exercises, divide the monomials. 288. 15r4s9(15r4s9)In the following exercises, divide the monomials. 289. 20m8n4(30m5n9)In the following exercises, divide the monomials. 290. 18a4b827a9b5In the following exercises, divide the monomials. 291. 45x5y960x8y6In the following exercises, divide the monomials. 292. (10m5n4)(5m3n6)25m7n5In the following exercises, divide the monomials. 293. (18p4q7)(6p3q8)36p12q10In the following exercises, divide the monomials. 294. (6a4b3)(4ab5)(12a2b)(a3b)In the following exercises, divide the monomials. 295. (4u2v5)(15u3v)(12u3v)(u4v)In the following exercises, divide each polynomial by the monomial. 296. (9n4+6n3)3nIn the following exercises, divide each polynomial by the monomial. 297. (8x3+6x2)2xIn the following exercises, divide each polynomial by the monomial. 298. (63m442m3)(7m2)In the following exercises, divide each polynomial by the monomial. 299. (48y424y3)(8y2)In the following exercises, divide each polynomial by the monomial. 300. 66x3y2110x2y344x4y311x2y2In the following exercises, divide each polynomial by the monomial. 301. 72r5s2+132r4s396r3s512r2s2In the following exercises, divide each polynomial by the monomial. 302. 10x2+5x45xIn the following exercises, divide each polynomial by the monomial. 303. 20y2+12y14yIn the following exercises, divide each polynomial by the binomial. 304. (y2+7y+12)(y+3)In the following exercises, divide each polynomial by the binomial. 305. (a22a35)(a+5)In the following exercises, divide each polynomial by the binomial. 306. (6m219m20)(m4)In the following exercises, divide each polynomial by the binomial. 307. (4x217x15)(x5)In the following exercises, divide each polynomial by the binomial. 308. (q2+2q+20)(q+6)In the following exercises, divide each polynomial by the binomial. 309. (p2+11p+16)(p+8)In the following exercises, divide each polynomial by the binomial. 310. (3b3+b2+4)(b+1)In the following exercises, divide each polynomial by the binomial. 311. (2n310n+28)(n+3)In the following exercises, divide each polynomial by the binomial. 312. (z3+1)(z+1)In the following exercises, divide each polynomial by the binomial. 313. (m3+1000)(m+10)In the following exercises, divide each polynomial by the binomial. 314. (64x327)(4x3)In the following exercises, divide each polynomial by the binomial. 315. (125y364)(5y4)In the following exercises, use synthetic Division to find the quotient and remainder. 316. x36x2+5x+14 is divided by x+1In the following exercises, use synthetic Division to find the quotient and remainder. 317. x33x24x+12 is divided by x+2In the following exercises, use synthetic Division to find the quotient and remainder. 318. 2x311x2+11x+12 is divided by x3In the following exercises, use synthetic Division to find the quotient and remainder. 319. 2x311x2+16x12 is divided by x4In the following exercises, use synthetic Division to find the quotient and remainder. 320. x4+13x2+13x+3 is divided by x+3In the following exercises, use synthetic Division to find the quotient and remainder. 321. x4+x2+6x10 is divided by x+2In the following exercises, use synthetic Division to find the quotient and remainder. 322. 2x49x3+5x23x6 is divided by x4In the following exercises, use synthetic Division to find the quotient and remainder. 323. 3x411x3+2x2+10x+6 is divided by x3In the following exercises, divide. 324. For functions f(x)=x213x+36 and g(x)=x4 , find (a) (fg)(x) (b) (fg)(1)In the following exercises, divide. 325. For functions f(x)=x215x+45 and g(x)=x9 , find (a) (fg)(x) (b) (fg)(5)In the following exercises, divide. 326. For functions f(x)=x3+x27x+2 and g(x)=x2 , find (a) (fg)(x) (b) (fg)(2)In the following exercises, divide. 327. For functions f(x)=x3+2x219x+12 and g(x)=x3 , find (a) (fg)(x) (b) (fg)(0)In the following exercises, divide. 328. For functions f(x)=x25x+2 and g(x)=x23x1 , find (a) (fg)(x) (b) (fg)(1)In the following exercises, divide. 329. For functions f(x)=x2+4x3 and g(x)=x2+2x+4 , find (a) (fg)(x) (b) (fg)(1)In the following exercises, use the Remainder Theorem to find the remainder. 330. f(x)=x38x+7 is divided by x+3In the following exercises, use the Remainder Theorem to find the remainder. 331. f(x)=x34x9 is divided by x+2In the following exercises, use the Remainder Theorem to find the remainder. 332. f(x)=2x36x24 is divided by x3In the following exercises, use the Remainder Theorem to find the remainder. 333. f(x)=7x25x8 is divided by x1In the following exercises, use the Factor Theorem to determine if xcis a factor of the polynomial function. 334. Determine whether x+3 a factor of x3+8x2+21x+18In the following exercises, use the Factor Theorem to determine if xcis a factor of the polynomial function. 335. Determine whether x+4 a factor of x3+x214x+8In the following exercises, use the Factor Theorem to determine if xcis a factor of the polynomial function. 336. Determine whether x2 a factor of x37x2+7x6In the following exercises, use the Factor Theorem to determine if xcis a factor of the polynomial function. 337. Determine whether x3 a factor of x37x2+11x+3James divides 48y+6 by 6 this way: 48+66=48y . What is wrong with his reasoning?Divide 10x2+x122x and explain with words how you get each term of the quotient.Explain when you can use synthetic division.In your own words, write the steps for synthetic division for x2+5x+6 divided by x2 .In the following exercises, determine the type of polynomial. 342. 16x240x25In the following exercises, determine the type of polynomial. 343. 5m+9In the following exercises, determine the type of polynomial. 344. 15In the following exercises, determine the type of polynomial. 345. y2+6y3+9y4In the following exercises, add or subtract the polynomials. 346. 4p+11pIn the following exercises, add or subtract the polynomials. 347. 8y35y3In the following exercises, add or subtract the polynomials. 348. (4a2+9a11)+(6a25a+10)In the following exercises, add or subtract the polynomials. 349. (8m2+12m5)(2m27m1)In the following exercises, add or subtract the polynomials. 350. (y23y+12)+(5y29)In the following exercises, add or subtract the polynomials. 351. (5u2+8u)(4u7)In the following exercises, add or subtract the polynomials. 352. Find the sum of 8q327 and q2+6q2 .In the following exercises, add or subtract the polynomials. 353. Find the sum of x2+6x+8 and x28x+15 .In the following exercises, simplify. 354. 17mn2(9mn2)+3mn2In the following exercises, simplify. 355. 18a7b21aIn the following exercises, simplify. 356. 2pq25p3q2In the following exercises, simplify. 357. (6a2+7)+(2a25a9)In the following exercises, simplify. 358. (3p24p9)+(5p2+14)In the following exercises, simplify. 359. (7m22m5)(4m2+m8)In the following exercises, simplify. 360. (7b24b+3)(8b25b7)In the following exercises, simplify. 361. Subtract (8y2y+9) from (11y29y5)In the following exercises, simplify. 362. Find the difference of (z24z12) and (3z2+2z11) .In the following exercises, simplify. 363. (x3x2y)(4xy2y3)+(3x2yxy2)In the following exercises, simplify. 364. (x32x2y)(xy23y3)(x2y4xy2)In the following exercises, find the function values for each polynomial function. 365. For the function f(x)=7x23x+5 find: (a) f(5) (b) f(2) (c) f(0)In the following exercises, find the function values for each polynomial function. 366. For the function g(x)=1516x2 find: (a) g(1) (b) g(0) (c) g(2)In the following exercises, find the function values for each polynomial function. 367. A pair of glasses is dropped off a bridge 640 feet above a river. The polynomial function h(t)=16t2+640 gives the height of the glasses t seconds after they were dropped. Find the height of the glasses when t=6 .In the following exercises, find the function values for each polynomial function. 368. A manufacturer of the latest soccer shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial R(p)=5p2+360p . Find the revenue received when p=110 dollars.In the following exercises, find (a) (f+g)(x)(b) (f+g)(3)(c) (fg)(x)(d) (fg)(2) 369. f(x)=2x24x7 and g(x)=2x2x+5In the following exercises, find (a) (f+g)(x)(b) (f+g)(3)(c) (fg)(x)(d) (fg)(2) 370. f(x)=4x33x2+x1 and g(x)=8x31In the following exercises, simplify each expression using the properties for exponents. 371. p3p10In the following exercises, simplify each expression using the properties for exponents. 372. 226In the following exercises, simplify each expression using the properties for exponents. 373. aa2a3In the following exercises, simplify each expression using the properties for exponents. 374. xx8In the following exercises, simplify each expression using the properties for exponents. 375. yaybIn the following exercises, simplify each expression using the properties for exponents. 376. 2822In the following exercises, simplify each expression using the properties for exponents. 377. a6aIn the following exercises, simplify each expression using the properties for exponents. 378. n3n12In the following exercises, simplify each expression using the properties for exponents. 379. 1x5In the following exercises, simplify each expression using the properties for exponents. 380. 30In the following exercises, simplify each expression using the properties for exponents. 381. y0In the following exercises, simplify each expression using the properties for exponents. 382. (14t)0In the following exercises, simplify each expression using the properties for exponents. 383. 12a015b0In the following exercises, simplify each expression. 384. 62In the following exercises, simplify each expression. 385. (10)3In the following exercises, simplify each expression. 386. 524In the following exercises, simplify each expression. 387. (8n)1In the following exercises, simplify each expression. 388. y5In the following exercises, simplify each expression. 389. 103In the following exercises, simplify each expression. 390. 1a4In the following exercises, simplify each expression. 391. 162In the following exercises, simplify each expression. 392. 53In the following exercises, simplify each expression. 393. (15)3In the following exercises, simplify each expression. 394. (12)3In the following exercises, simplify each expression. 395. (5)3In the following exercises, simplify each expression. 396. (59)2In the following exercises, simplify each expression. 397. (3x)3In the following exercises, simplify each expression using the Product Property. 398. (y4)3In the following exercises, simplify each expression using the Product Property. 399. (32)5In the following exercises, simplify each expression using the Product Property. 400. (a 10)yIn the following exercises, simplify each expression using the Product Property. 401. x3x9In the following exercises, simplify each expression using the Product Property. 402. r5r4In the following exercises, simplify each expression using the Product Property. 403. (uv3)(u4v2)In the following exercises, simplify each expression using the Product Property. 404. (m5)1In the following exercises, simplify each expression using the Product Property. 405. p5p2p4In the following exercises, simplify each expression using the Power Property. 406. (k 2)3In the following exercises, simplify each expression using the Power Property. 407. q4q20In the following exercises, simplify each expression using the Power Property. 408. b8b2In the following exercises, simplify each expression using the Power Property. 409. n3n5In the following exercises, simplify each expression using the Product to a Power Property. 410. (5ab)3In the following exercises, simplify each expression using the Product to a Power Property. 411. (4pq)0In the following exercises, simplify each expression using the Product to a Power Property. 412. (6x3)2In the following exercises, simplify each expression using the Product to a Power Property. 413. (3y 4)2In the following exercises, simplify each expression using the Quotient to a Power Property. 414. (3 5x)2In the following exercises, simplify each expression using the Quotient to a Power Property. 415. ( 3x y 2 z)4In the following exercises, simplify each expression using the Quotient to a Power Property. 416. ( 4 p 3 q 2 )2In the following exercises, simplify each expression by applying several properties. 417. (x2y)2(3xy5)3In the following exercises, simplify each expression by applying several properties. 418. ( 3 a 2 )4( 2 a 4 )2( 6 a 2 )3In the following exercises, simplify each expression by applying several properties. 419. ( 3x y 3 4 x 4 y 2 )2( 6x y 4 8 x 3 y 2 )1In the following exercises, write each number in scientific notation. 420. 2.568In the following exercises, write each number in scientific notation. 421. 5,300,000In the following exercises, write each number in scientific notation. 422. 0.00814In the following exercises, convert each number to decimal form. 423. 2.9104In the following exercises, convert each number to decimal form. 424. 3.75101In the following exercises, convert each number to decimal form. 425. 9.413105In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 426. (3107)(2104)In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 427. (1.5103)(4.8101)In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 428. 61092101In the following exercises, multiply or divide as indicated. Write your answer in decimal form. 429. 91031106In the following exercises, multiply the monomials. 430. (6p4)(9p)In the following exercises, multiply the monomials. 431. (13c2)(30c8)In the following exercises, multiply the monomials. 432. (8x2y5)(7xy6)In the following exercises, multiply the monomials. 433. (23m3n6)(16m4n4)In the following exercises, multiply. 434. 7(10x)In the following exercises, multiply. 435. a2(a29a36)In the following exercises, multiply. 436. 5y(125y31)In the following exercises, multiply. 437. (4n5)(2n3)In the following exercises, multiply the binomials using:(a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 438. (a+5)(a+2)In the following exercises, multiply the binomials using: (a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 439. (y4)(y+12)In the following exercises, multiply the binomials using: (a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 440. (3x+1)(2x7)In the following exercises, multiply the binomials using:(a) the Distributive Property (b) the FOIL method (c) the Vertical Method. 441. (6p11)(3p10)In the following exercises, multiply the binomials. Use any method. 442. (n+8)(n+1)In the following exercises, multiply the binomials. Use any method. 443. (k+6)(k9)In the following exercises, multiply the binomials. Use any method. 444. (5u3)(u+8)In the following exercises, multiply the binomials. Use any method. 445. (2y9)(5y7)In the following exercises, multiply the binomials. Use any method. 446. (p+4)(p+7)In the following exercises, multiply the binomials. Use any method. 447. (x8)(x+9)In the following exercises, multiply the binomials. Use any method. 448. (3c+1)(9c4)In the following exercises, multiply the binomials. Use any method. 449. (10a1)(3a3)In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method. 450. (x+1)(x23x21)In the following exercises, multiply using (a) the Distributive Property (b) the Vertical Method. 451. (5b2)(3b2+b9)In the following exercises, multiply. Use either method. 452. (m+6)(m27m30)In the following exercises, multiply. Use either method. 453. (4y1)(6y212y+5)In the following exercises, square each binomial using the Binomial Squares Pattern. 454. (2xy2)In the following exercises, square each binomial using the Binomial Squares Pattern. 455. (x+34)2In the following exercises, square each binomial using the Binomial Squares Pattern. 456. (8p33)2In the following exercises, square each binomial using the Binomial Squares Pattern. 457. (5p+7q)2In the following exercises, multiply each pair of conjugates using the Product of Conjugates. 458. (3y+5)(3y5)In the following exercises, multiply each pair of conjugates using the Product of Conjugates. 459. (6x+y)(6xy)In the following exercises, multiply each pair of conjugates using the Product of Conjugates. 460. (a+23b)(a23b)In the following exercises, multiply each pair of conjugates using the Product of Conjugates. 461. (12x37y2)(12x3+7y2)In the following exercises, multiply each pair of conjugates using the Product of Conjugates. 462. (13a28b4)(13a2+8b4)In the following exercises, divide the monomials. 463. 72p128p3In the following exercises, divide the monomials. 464. 26a8(2a2)In the following exercises, divide the monomials. 465. 45y615y10In the following exercises, divide the monomials. 466. 30x836x9In the following exercises, divide the monomials. 467. 28a9b7a4b3In the following exercises, divide the monomials. 468. 11u6v355u2v8In the following exercises, divide the monomials. 469. (5m9n3)(8m3n2)(10mn4)(m2n5)In the following exercises, divide the monomials. 470. (42r2s4)(54rs2)(6rs3)(9s)In the following exercises, divide each polynomial by the monomial 471. (54y424y3)(6y2)In the following exercises, divide each polynomial by the monomial 472. 63x3y299x2y345x4y39x2y2In the following exercises, divide each polynomial by the monomial 473. 12x2+4x34xIn the following exercises, divide each polynomial by the binomial. 474. (4x221x18)(x6)In the following exercises, divide each polynomial by the binomial. 475. (y2+2y+18)(y+5)In the following exercises, divide each polynomial by the binomial. 476. (n32n26n+27)(n+3)In the following exercises, divide each polynomial by the binomial. 477. (a31)(a+1)In the following exercises, use synthetic Division to find the quotient and remainder. 478. x33x24x+12 is divided by x+2In the following exercises, use synthetic Division to find the quotient and remainder. 479. 2x311x2+11x+12 is divided by x3In the following exercises, use synthetic Division to find the quotient and remainder. 480. x4+x2+6x10 is divided by x+2In the following exercises, divide. 481. For functions f(x)=x215x+45 and g(x)=x9 , find (a) (fg)(x) (b) (fg)(2)In the following exercises, divide. 482. For functions f(x)=x3+x27x+2 and g(x)=x2 , find (a) (fg)(x) (b) (fg)(3)In the following exercises, use the Remainder Theorem to find the remainder. 483. f(x)=x34x9 is divided by x+2In the following exercises, use the Remainder Theorem to find the remainder. 484. f(x)=2x36x24 is divided by x3In the following exercises, use the Factor Theorem to determine if xcis a factor of the polynomial function. 485. Determine whether x2 is a factor of x37x2+7x6 .In the following exercises, use the Factor Theorem to determine if xcis a factor of the polynomial function. 486. Determine whether x3 is a factor of x37x2+11x+3 .For the polynomial 8y43y2+1 (a) Is it a monomial, binomial, or trinomial? (b) What is its degree?(5a2+2a12)(9a2+8a4)(10x23x+5)(4x26)(34)3x3x45658(47a18b23c5)041(2y)3p3p8x4x5(3x3)224r3s6r2s7( x 4 y 9 x 3)2(8xy3)(6x4y6)4u(u29u+1)(m+3)(7m2)(n8)(n24n+11)(4x3)2(5x+2y)(5x2y)(15xy335x2y)5xy(3x310x2+7x+10)(3x+2)Use the Factor Theorem to determine if x+3 a factor of x3+8x2+21x+18 .(a) Convert 112,000 to scientific notation. (b) Convert 5.25104 to decimal form.In the following exercises, simplify and write your answer in decimal form. 511. (2.4108)(2105)In the following exercises, simplify and write your answer in decimal form. 512. 91043101In the following exercises, simplify and write your answer in decimal form. 513. For the function f(x)=6x23x9 find: (a) f(3) (b) f(2) (c) f(0)In the following exercises, simplify and write your answer in decimal form. 514. For f(x)=2x23x5 and g(x)=3x24x+1 , find (a) (f+g)(x) (b) (f+g)(1) (c) (fg)(x) (d) (fg)(2)In the following exercises, simplify and write your answer in decimal form. 515. For functions f(x)=3x223x36 and g(x)=x9, find (a) (fg)(x) (b) (fg)(3)In the following exercises, simplify and write your answer in decimal form. 516. A hiker drops a pebble from a bridge 240 feet above a canyon. The function h(t)=16t2+240 gives the height of the pebble t seconds after it was dropped. Find the height when t=3 .Find the greatest common factor: 25m4,35m3,20m2 .Find the greatest common factor: 14x3,70x2,105x .Factor: 9xy2+6x2y2+21y3 .Factor: 3p36p2q+9pq3 .Factor: 2x3+12x2 .Factor: 6y315y2 .Factor: 15x3y3x2y2+6xy3 .Factor: 8a3b+2a2b26ab3 .Factor: 4b3+16b28b .Factor: 7a3+21a214a .Factor: 4m(m+3)7(m+3) .Factor: 8n(n4)+5(n4) .Factor by grouping: xy+8y+3x+24 .Factor by grouping: ab+7b+8a+56 .Factor by grouping: (a) x2+2x5x10 (b ) 20x216x15x+12 .Factor by grouping: (a) y2+4y7y28 (b) 42m218m35m+15 .In the following exercises, find the greatest common factor. 1. 10p3q,12pq2In the following exercises, find the greatest common factor. 2. 8a2b3,10ab2In the following exercises, find the greatest common factor. 3. 12m2n3,30m5n3In the following exercises, find the greatest common factor. 4. 28x2y4,42x4y4In the following exercises, find the greatest common factor. 5. 10a3,12a2,14aIn the following exercises, find the greatest common factor. 6. 20y3,28y2,40yIn the following exercises, find the greatest common factor. 7. 35x3y2,10x4y,5x5y3In the following exercises, find the greatest common factor. 8. 27p2q3,45p3q4,9p4q3In the following exercises, factor the greatest common factor from each polynomial. 9. 6m+9In the following exercises, factor the greatest common factor from each polynomial. 10. 14p+35In the following exercises, factor the greatest common factor from each polynomial. 11. 9n63In the following exercises, factor the greatest common factor from each polynomial. 12. 45b18In the following exercises, factor the greatest common factor from each polynomial. 13. 3x2+6x9In the following exercises, factor the greatest common factor from each polynomial. 14. 4y2+8y4In the following exercises, factor the greatest common factor from each polynomial. 15. 8p2+4p+2In the following exercises, factor the greatest common factor from each polynomial. 16. 10q2+14q+20In the following exercises, factor the greatest common factor from each polynomial. 17. 8y3+16y2In the following exercises, factor the greatest common factor from each polynomial. 18. 12x310xIn the following exercises, factor the greatest common factor from each polynomial. 19. 5x315x2+20xIn the following exercises, factor the greatest common factor from each polynomial. 20. 8m240m+16In the following exercises, factor the greatest common factor from each polynomial. 21. 24x312x2+15xIn the following exercises, factor the greatest common factor from each polynomial. 22. 24y318y230yIn the following exercises, factor the greatest common factor from each polynomial. 23. 12xy2+18x2y230y3In the following exercises, factor the greatest common factor from each polynomial. 24. 21pq2+35p2q228q3In the following exercises, factor the greatest common factor from each polynomial. 25. 20x3y4x2y2+12xy3In the following exercises, factor the greatest common factor from each polynomial. 26. 24a3b+6a2b218ab3In the following exercises, factor the greatest common factor from each polynomial. 27. 2x4In the following exercises, factor the greatest common factor from each polynomial. 28. 3b+12In the following exercises, factor the greatest common factor from each polynomial. 29. 2x3+18x28xIn the following exercises, factor the greatest common factor from each polynomial. 30. 5y3+35y215yIn the following exercises, factor the greatest common factor from each polynomial. 31. 4p3q12p2q2+16pq2In the following exercises, factor the greatest common factor from each polynomial. 32. 6a3b12a2b2+18ab2In the following exercises, factor the greatest common factor from each polynomial. 33. 5x(x+1)+3(x+1)In the following exercises, factor the greatest common factor from each polynomial. 34. 2x(x1)+9(x1)In the following exercises, factor the greatest common factor from each polynomial. 35. 3b(b2)13(b2)In the following exercises, factor the greatest common factor from each polynomial. 36. 6m(m5)7(m5)In the following exercises, factor by grouping. 37. ab+5a+3b+15In the following exercises, factor by grouping. 38. cd+6c+4d+24In the following exercises, factor by grouping. 39. 8y2+y+40y+5In the following exercises, factor by grouping. 40. 6y2+7y+24y+28In the following exercises, factor by grouping. 41. uv9u+2v18In the following exercises, factor by grouping. 42. pq10p+8q80