Question Completion Status: QUESTION 1 Factoring polynomial functions f(x)=x6-3x4 + 2x². g(x)=x3-5x2-x+ 5 ✓h(x) = x3+4x²+x-6 ✓k(x)=x4-19x² + 30x QUESTION 2 Find the quotient (x² + 9x+20) + (x+5) ✓ Write the division as a long division problem. ✓ Divide x² by x ✓Multiply x + 5 by x: Subtract x² + 5x from x2 + 5x + 20: ✓Multiply x + 5 by 4: Subtract 4x + 20 from 4x + 20 What is the remainder ? What is the quotient ? a. x(x-2)(x - 3)(x + 5) b. NA c.x²(x2-1)(x²-2) d. (x - 5)(x-1)(x + 1) e. Undefined f. (x+3)(x + 2)(x-1) 1. x+5)x² + 9x+20 x+5x 2. 4x+20 3. NA 4. X+4 6. X+4 x+5) x+ 9x+20 -x+(-5x) 4x + 20 x + 4 x+5) x²+ 9x+ 20 x+(-5x) 4x+ 20 -4x+(-20) 7. 0 8. x+5)x+ 9x + 20 9. x+5)x¹+9x+ 20 10. Undefined 0
Question Completion Status: QUESTION 1 Factoring polynomial functions f(x)=x6-3x4 + 2x². g(x)=x3-5x2-x+ 5 ✓h(x) = x3+4x²+x-6 ✓k(x)=x4-19x² + 30x QUESTION 2 Find the quotient (x² + 9x+20) + (x+5) ✓ Write the division as a long division problem. ✓ Divide x² by x ✓Multiply x + 5 by x: Subtract x² + 5x from x2 + 5x + 20: ✓Multiply x + 5 by 4: Subtract 4x + 20 from 4x + 20 What is the remainder ? What is the quotient ? a. x(x-2)(x - 3)(x + 5) b. NA c.x²(x2-1)(x²-2) d. (x - 5)(x-1)(x + 1) e. Undefined f. (x+3)(x + 2)(x-1) 1. x+5)x² + 9x+20 x+5x 2. 4x+20 3. NA 4. X+4 6. X+4 x+5) x+ 9x+20 -x+(-5x) 4x + 20 x + 4 x+5) x²+ 9x+ 20 x+(-5x) 4x+ 20 -4x+(-20) 7. 0 8. x+5)x+ 9x + 20 9. x+5)x¹+9x+ 20 10. Undefined 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Just give me the answers in order like
1-
2-
3-
Etc
Please but also you can explain if you want
Transcribed Image Text:**QUESTION 1**
Factoring polynomial functions:
- \( f(x) = 6 - 3x^4 + 2x^2 \)
- \( g(x) = 3 - 5x^2 - x + 5 \)
- \( h(x) = x^3 + 4x^2 + x - 6 \)
- \( k(x) = x^4 - 19x^2 + 30x \)
Options:
- a. \( x(x - 2)(x - 3)(x + 5) \)
- b. NA
- c. \( x^2(x^2 - 1)(x^2 - 2) \)
- d. \( (x - 5)(x - 1)(x + 1) \)
- e. Undefined
- f. \( (x + 3)(x + 2)(x - 1) \)
**QUESTION 2**
Find the quotient \( \frac{x^2 + 9x + 20}{x + 5} \)
Steps:
1. Write the division as a long division problem.
2. Divide \( x^2 \) by \( x \).
3. Multiply 1st by \( x \).
4. Subtract \( x^2 - 5x \) from \( x^2 + 5x + 20 \).
5. Multiply \( x + 5 \) by 4.
6. Subtract \( 4x + 20 \) from \( 4x + 20 \).
7. What is the remainder?
8. What is the quotient?
Equation breakdown shown in steps:
1. Divide \( x^2 + 9x + 20 \) by \( x + 5 \).
2. \( x + 4 \) is obtained.
3. Subtract and solve further:
- Result: Remainder is 0.
The division results in no remainder and the quotient \( x + 4 \). The process shown indicates proper completion of polynomial division without issues.
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