Question

If the polynomial 2x³ + 3x² – 2x – 3 is completely divisible by (2x + a) and the quotient is equal to (x² – 1), then one of the values of a is ______.

Options

• –3

• –1

• 1

• 3

Answer 1

If the polynomial 2x³ + 3x² – 2x – 3 is completely divisible by (2x + a) and the quotient is equal to (x² – 1), then one of the values of a is 3.

Explanation:

(2x + a)(x² – 1) = 2x³ + ax² – 2x – a.

This must equal 2x³ + 3x² – 2x – 3, so comparing coefficients gives a = 3 and –a = –3, consistent.

Hence, a = 3.