Question

1.(03.02)

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 1

no

Explanation:

By the factor theorem

If (x + h) is a factor of f(x) then f(- h) = 0

Given (x + 4) with h = - 4 , then

f(- 4) = (- 4)³ - 2(- 4)² + 5(- 4) + 1

= - 64 - 2(16) - 20 + 1

= - 64 - 32 - 19

= - 115

Since f(- 4) ≠ 0 then (x + 4) is not a factor of f(x)