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_3. Which polynomial gives a quotient of (3x² + 2x + 4) and a remainder of 19 when divided by 2x - 32 A. 6x3 – 5x2 + 2x B. C. 6x3 – 5x2 + 4x + 7 D. 6x3 + 5x2 + 2x +7 6x3 – 5x2 + 2x + 7

_3. Which polynomial gives a quotient of (3x² + 2x + 4) and a remainder of 19 when divided by 2x - 32 A. 6x3 – 5x2 + 2x B. C. 6x3 – 5x2 + 4x + 7 D. 6x3 + 5x2 + 2x +7 6x3 – 5x2 + 2x + 7

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Division of Polynomials
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(DIVISION OF POLYNOMIALS) MULTIPLE CHOICE. Read each item carefully, analyze well and choose the correct answer. Write the letter that corresponds to your choice on space provided. 1. The leading coefficient of the polynomial 5x10 + 4x'2 + 4x6 + x* – x is_ A. 4 В. 5 С. 10 D. 12 _2. What is the quotient when x2 - 25 is divided by x- 5? A. x+ 5 _3. Which polynomial gives a quotient of (3x2 + 2x + 4) and a remainder of 19 when divided by 2x - 3? A. 6x - 5x? + 2x В. В. х - 5 С.х-1 D. x? + 5 C. 6x3 – 5x2 + 4x + 7 6x3 – 5x2 + 2x +7 D. 6x3 + 5x2 + 2x + 7 _4. Which of the following is a polynomial? i. x3 + 2x2 + 5x + 2 A. i only _5. The following are examples of polynomials, EXCEPT А. у2 - 4y + 5 B. 3r* – 5r + 2r -1 _6. Which of the following statements is NOT true about the Remainder Theorem? A. The remainder R is a constant and is equal to P(r) i. 5x° + 3x2 + x + 2 B. i only iii. V5x2 + V3x C.i and i D. i and i C. 5x3 + 9x2 + 12x +8 D. a- b B. The remainder R is equal to the constant term of the dividend. C. The remainder R is a constant and is equal to P(x) D. The remainder R is solved by substituting r in the polynomial P(x) _7. In the Factor Theorem, the polynomial P(x) has x -ras a factor if and only if P(1) is, A. Equal to P(x) _8. If P(-2) = 0, which of the following statements is true about P(x)? A. x + 2 is a factor of P(x) B. 2 is root of P(x) = 0 9. Which of the following is the degree of the polynomial equation x3 - 2x® - 4x + 8 = 0? B. equal to 0 C. Greater than 0 D. Equal to 1 C. P(x) = 0, has two negative roots D. P(0) = -2 A. 3 B. 12 C.11 D. 8 10. Given P(x) = 3x³ + 2x? – x. What is the value of P(2)? A. 20 В. 30 C. 40 D. 50 L11. What is the value of k so that (x – 3) will be a factor of (x³ + kx + 3)? A. -10 В. -12 C.-14 D. -16 _12. Gabriel will evaluate an 8th degree polynomial in x at x = 10 using synthetic division. How many coefficients of x will be written in the first row of the synthetic division procedure? A. 8 C. 10 D. 11 В. 9 _13. A car manufacturer determines that its profit, P, in thousands of pesos, can be modeled by the function P(x) = 0.00125x + x - 3, where x represents the number of cars sold. What is the profit at x = 150? A. Php 75.28B. Php 632, 959.50 C. Php 3,000,000.00 D. Php 10, 125, 297.00 _14. A demographer predicts that the population, P, of a town t years from now can be modeled by the function P(t) = 6t4 - 5t3 + 200t + 12 000. What will the population of the town be two (2) years from now? A. 12, 456 C. 1 245 600 15. What is the remainder when (5x'00 + 5) is divided by (x – 1)? A. 5 В. 124 560 D. 12 456 000 B. 10 C. -5 D. -10
Transcribed Image Text:(DIVISION OF POLYNOMIALS) MULTIPLE CHOICE. Read each item carefully, analyze well and choose the correct answer. Write the letter that corresponds to your choice on space provided. 1. The leading coefficient of the polynomial 5x10 + 4x'2 + 4x6 + x* – x is_ A. 4 В. 5 С. 10 D. 12 _2. What is the quotient when x2 - 25 is divided by x- 5? A. x+ 5 _3. Which polynomial gives a quotient of (3x2 + 2x + 4) and a remainder of 19 when divided by 2x - 3? A. 6x - 5x? + 2x В. В. х - 5 С.х-1 D. x? + 5 C. 6x3 – 5x2 + 4x + 7 6x3 – 5x2 + 2x +7 D. 6x3 + 5x2 + 2x + 7 _4. Which of the following is a polynomial? i. x3 + 2x2 + 5x + 2 A. i only _5. The following are examples of polynomials, EXCEPT А. у2 - 4y + 5 B. 3r* – 5r + 2r -1 _6. Which of the following statements is NOT true about the Remainder Theorem? A. The remainder R is a constant and is equal to P(r) i. 5x° + 3x2 + x + 2 B. i only iii. V5x2 + V3x C.i and i D. i and i C. 5x3 + 9x2 + 12x +8 D. a- b B. The remainder R is equal to the constant term of the dividend. C. The remainder R is a constant and is equal to P(x) D. The remainder R is solved by substituting r in the polynomial P(x) _7. In the Factor Theorem, the polynomial P(x) has x -ras a factor if and only if P(1) is, A. Equal to P(x) _8. If P(-2) = 0, which of the following statements is true about P(x)? A. x + 2 is a factor of P(x) B. 2 is root of P(x) = 0 9. Which of the following is the degree of the polynomial equation x3 - 2x® - 4x + 8 = 0? B. equal to 0 C. Greater than 0 D. Equal to 1 C. P(x) = 0, has two negative roots D. P(0) = -2 A. 3 B. 12 C.11 D. 8 10. Given P(x) = 3x³ + 2x? – x. What is the value of P(2)? A. 20 В. 30 C. 40 D. 50 L11. What is the value of k so that (x – 3) will be a factor of (x³ + kx + 3)? A. -10 В. -12 C.-14 D. -16 _12. Gabriel will evaluate an 8th degree polynomial in x at x = 10 using synthetic division. How many coefficients of x will be written in the first row of the synthetic division procedure? A. 8 C. 10 D. 11 В. 9 _13. A car manufacturer determines that its profit, P, in thousands of pesos, can be modeled by the function P(x) = 0.00125x + x - 3, where x represents the number of cars sold. What is the profit at x = 150? A. Php 75.28B. Php 632, 959.50 C. Php 3,000,000.00 D. Php 10, 125, 297.00 _14. A demographer predicts that the population, P, of a town t years from now can be modeled by the function P(t) = 6t4 - 5t3 + 200t + 12 000. What will the population of the town be two (2) years from now? A. 12, 456 C. 1 245 600 15. What is the remainder when (5x'00 + 5) is divided by (x – 1)? A. 5 В. 124 560 D. 12 456 000 B. 10 C. -5 D. -10
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