Question

If x² + x + 1 is a factor of the polynomial 3x³ + 8x² + 8x + a, then find the value of a.

Answer 1

Given that x² + x + 1 is a factor of the polynomial 3x³ + 8x² + 8x + a

∴ 3x³ + 8x² + 8x + a is divisible by x² + x + 1

Since 3x³ + 8x² + 8x + a is divisible by x² + x + 1

The remainder must be zero.

a – 5 = 0

⇒ a = 5