107k views
3 votes
Use Remainder Theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5 - 7x^3 -

11x^2 + 2

Use Remainder Theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5 - 7x-example-1
User Wiherek
by
8.3k points

2 Answers

5 votes

Answer:

Answers to the Complex Zeroes of a Polynomial Function Quiz Part 1 (I tried to signify each question)

Explanation:

1. C, f(x) is a polynomial function. The degree is 5... -7

2. A, f(x)=7x^9-3x^2-6

3. C,D

4. Written

5. Rational Zero Theorem, B

6. Written

7. B, -5,-2, 3

8. A, (4 + 6i, -2 -11i)

9. D, (2,3, plus minus sqrt 5i)

User Thilina Koggalage
by
8.8k points
3 votes

Answer:

(x - 2) is not a factor of f(x) = 3x^5 - 7x^3 - 11x^2 + 2

Explanation:

According to the Remainder Theorem, when a polynomial f(x) is divided by a term (x - r), then the remainder must be f(r).

So first we will divide f(x) by (x - 2) using long division to get:

(3x^5 - 7x^3 - 11x^2 + 2) / (x - 2)

= 3x^4 + (6x^4 - 7x^3 - 11x^2 + 2) / (x-2)

= 3x^4 + 6x^3 + (5x^3-11x^2+2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 (-x^2 + 2) / (x - 2)

= 3x^4 + 6x^3 + 5x^2 -x -2 - (2) / (x -2)

=
(-2 + 3x^(5) - 7x^(3) - 11x^(2) + 2x)/(x - 2) - 2

Therefore the remainder is -2.

Now check x = 2 for 3x^5 - 7x^3 - 11x^2 + 2:

3(2)^5 - 7(2)^3 - 11(2)^2 + 2 = -2

The Remainder Factor theorem also states that if (x - r) is a factor of f(x) then f(r) must be 0.

So we found that f(2) = -2, therfore (x - 2) is not a factor of f(x) .


User Zlack
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories