The polynomial 2x³ + ax² + bx − 6 has (x − 2) as a factor and leaves remainder −15 on division by (x + 1). Find ab.

Question

Accepted Answer

−12. f(2) = 16 + 4a + 2b − 6 = 0 gives 2a + b = −5. f(−1) = −2 + a − b − 6 = −15 gives a − b = −7. Adding, 3a = −12, so a = −4, b = 3 and ab = −12.

The polynomial $2 x^{3} + a x^{2} + b x - 6$ has $(x - 2)$ as a factor and leaves remainder −15 on division by $(x + 1)$ . Find $ab$ .