If f(x) = -x^2 + 3x - 2, which of the following is a factor of f(x)?
A. (x^2 + 6)
B. (x - 1)
C. (2x - 5)
D. (x + 1)

Question

Accepted Answer

f(x) = -(x-1)(x-2), so (x-1) is a factor of f(x). A polynomial p(x) has a factor (x - a) if and only if p(a) = 0 (Factor Theorem). We can test each option by substituting the root into f(x), or factorize f(x) directly. Since f(x) = -x^2 + 3x - 2 = -(x^2 - 3x + 2) = -(x-1)(x-2), both (x-1) and (x-2) are factors.

If f(x) = -x^2 + 3x - 2, which of the following is a factor of f(x)? A. (x^2 + 6) B. (x - 1) C. (2x - 5) D. (x + 1)