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.

I pretty confused on this I thought it was no at first but I dont know anymore can someboyd help

1 answer

If for some function f(a) = 0 , then x-a is a factor

so you were testing if x - 3 is a factor, then f(3) = 0