Is (x − 4) a factor of f(x) = x3 − 2x2 + 5x + 1? use either the remainder theorem or the factor theorem to explain your reasoning.

ANSWER

Not a factor

EXPLANATION

The given polynomial function is

According to the remainder theorem, if f(x) is divided by (x-4), the remainder is f(4).

We plug in x=4 to obtain:

According to the factor Theorem, the remainder must be zero for x-4 to be a factor of f(x).

Since the remainder is not zero, x-4 is not a factor of f(x).

answer: 1 + 1 = 11

step-by-step explanation: