Question
The polynomial p(x) = kx3 + 9x2 + 4x - 8 when divided by x + 3 leaves a remainder - 20. Find the value of k.
Solution
Divisor = x + 3
x + 3 = 0 ⇒ x = - 3
∴ Zero of x + 3 is - 3
Remainder = -20 | Given
⇒ p(- 3) = -20
⇒ k(- 3)3 + 9(- 3)2 + 4(- 3) - 8 = - 20
⇒ - 27k + 81 - 12 - 8 = - 20
⇒ 27k = 81
⇒ k = 3.
