Question

If x + α is a factor of the polynomial 2x² + 2αx + 4x + 12, then α = ______.

Answer 1

If x + α is a factor of the polynomial 2x² + 2αx + 4x + 12, then α = 3.

Explanation:

The polynomial is 2x² + (2α + 4)x + 12. If x + α is a factor, set x = –α and equate to zero:

2(–α)² + (2α + 4)(–α) + 12 = 0

⇒ 2α² – 2α² – 4α + 12 = 0

⇒ –4α + 12 = 0

⇒ α = 3