The remainder when p(x) = kx^3 + 3x^2 - 3 is divided by (x - 2) equals the remainder when q(x) = 2x^3 + 5x + 7k is divided by (x - 2). Find k.

Question

Accepted Answer

17. p(2) = 8k + 12 - 3 = 8k + 9. q(2) = 16 + 10 + 7k = 7k + 26. Set equal: 8k + 9 = 7k + 26, so k = 17.

The remainder when $p (x) = k x^{3} + 3 x^{2} - 3$ is divided by $(x - 2)$ equals the remainder when $q (x) = 2 x^{3} + 5 x + 7 k$ is divided by $(x - 2)$ .
Find $k$ .