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?

no

Step-by-step explanation:

The factor theorem states that if (x + h) is a factor of f (x) then f ( - h) = 0

Given

f (x) = x³ - 2x² + 5x + 1, then evaluating f (4)

f (4) = 4³ - 2 (4) ² + 5 (4) + 1 = 64 - 32 + 20 + 1 = 53 ≠ 0

Thus (x - 4) is not a factor of f (x)