Question

Is (x + 7) a factor of f(x) = x3 − 3x2 + 2x − 8

Answer 1

no

Explanation:

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

Thus if (x + 7) is a factor of f(x) then f(- 7) = 0

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

= - 343 - 147 - 14 - 8 = - 512 ≠ 0

Since f(- 7) ≠ 0 then (x + 7) is not a factor of f(x)