Question

Determine whether x + 1 is a factor of x³ + x² − 8x − 8.

Answer 1

Let f(x) = x³ + x² − 8x − 8

Let x + 1 = 0

x = −1

f(−1) = (−1)³ + (−1)² − 8(−1) − 8

= −1 + 1 + 8 − 8

= 0

Since f(−1) = 0, x + 1 is a factor of x³ + x² − 8x − 8.