Question

If p(x) = ax³ + 3x² + 7x + 13 is divided by (x + 3), then the remainder is - 8. Find the value of a.

Answer 1

$p(x) = a {x}^{3} + 3 {x}^{2} + 7x + 13 \\ according \: \: to \: \: remainder \: \: theorem \\ p( - 3) = - 8 \\ a \times {( - 3)}^{3} + 3 \times {( - 3)}^{2} + 7 \times - 3 + 13 = - 8 \\ - 27a = - 27 \\ a = 1$