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
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
To determine if x-3 is a factor of f(x)=x^3+x^2-10x+8, we can use the Factor Theorem. According to the Factor Theorem, if x-a is a factor of a polynomial, then the polynomial evaluated at a should equal zero.
In this case, Devon evaluated f(-3) instead of f(3) to check if x-3 is a factor. Evaluating f(-3) gives:
f(-3) = (-3)^3 + (-3)^2 - 10(-3) + 8 = 27 + 9 + 30 + 8 = 74
Based on this evaluation, Devon concluded that the remainder is 20, which led her to believe that x-3 is not a factor of f(x).
However, Devon made a mistake in evaluating f(-3). The correct evaluation should be f(3) because we are checking if x-3 is a factor. Evaluating f(3) gives:
f(3) = (3)^3 + (3)^2 - 10(3) + 8 = 27 + 9 - 30 + 8 = 14
Since f(3) is not equal to zero, we can conclude that x-3 is not a factor of f(x).
Therefore, the correct answer is B. Yes, Devon evaluated f(-3) incorrectly.