Question

Is (x+2) a factor of f(x) = x3-7x2+2x-8? Use either remainder theorem to explain your reasoning

Answer 1

No

Explanation:

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

Here (x + 2) with h = - 2 , then

f(- 2) = (- 2)³ - 7(- 2)² + 2(- 2) - 8

= - 8 - 7(4) - 4 - 8

= - 8 - 28 - 12

= - 48

Since f(- 2) ≠ 0 then (x + 2) is not a factor of f(x)