Question

Find the value of p if x³ + 2x² − 6x + p is exactly divisible by x + 4.

Answer 1

Let f(x) = x³ + 2x² − 6x + p

Let x + 4 = 0

x = −4

f(−4) = 0

⇒ f(−4) = (−4)³ + 2(−4)² − 6(−4) + p = 0

⇒ −64 + 32 + 24 + p = 0

⇒ −8 + p = 0

⇒ p = 8