Question

If x + 1 is a factor of the polynomial 2x³ + ax² + 4x + 1, then a = ______.

Answer 1

If x + 1 is a factor of the polynomial 2x³ + ax² + 4x + 1, then a = 5.

Explanation:

If x + 1 is a factor, the polynomial must equal 0 at x = –1 (factor theorem). 

Evaluate: 2(–1)³ + a(–1)² + 4(–1) + 1

= –2 + a – 4 + 1 

= a – 5

Set a – 5 = 0, so a = 5.