## can yall help me out Devon wanted to know if x−3 is a factor of f(x)=x^3+x^2−10x+8. She applied the Factor Theorem and concluded

Question

can yall help me out

Devon wanted to know if x−3 is a factor of f(x)=x^3+x^2−10x+8. She applied the Factor Theorem and concluded that x−3 is not a factor of f(x), as shown in the following work.

f(−3)=(−3)^3+(−3)^2−10(−3)+8=20
f(−3)=20, so the remainder is 20.
The remainder is 20, so x−3 is not a factor of f(x).

Did Devon make a mistake? If so, what was her mistake?

A.Yes, x−3 is a factor of f(x).
B.Yes, Devon evaluated f(−3) incorrectly.
C.No, Devon did not may any mistakes.
D.Yes, Devon should have evaluated f(3).
E,Yes, f(−3)=20 does not mean the remainder is 20.

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2 weeks 2021-09-10T20:19:49+00:00 1 Answer 0

Option D, Yes, Devon should have evaluated f(3)

Step-by-step explanation:

f(x) = x^3 + x^2 − 10x + 8

Step 1:  Evaluate using F(3) NOT f(-3)

f(3) = 3^3 + 3^2 – 10(3) + 8

f(3) = 27 + 9 – 30 + 8

f(3) = 14

Since the factor is (x – 3) the x value is x – 3 + 3 = 0 + 3 -> x = 3 not x = -3

Answer:  Option D, Yes, Devon should have evaluated f(3)