Question

Is (x+4) a factor of the polynomial x^3+8x^2+11x-20? Explain

Answer 1

yes

Explanation:

if (x + a) is a factor of f(x), then f(- a) = 0, Factor theorem

given

f(x) = x³ + 8x² + 11x - 20

then if (x + 4) is a factor f(- 4) = 0

f(- 4) = (- 4)³ + 8(- 4)² + 11(- 4) - 20

= - 64 + 8(16) - 44 - 20

= - 64 + 128 - 64

= 0

since f(- 4) = 0 , then (x + 4) is a factor of the polynomial