Question

If the polynomial ax⁵ - 23x³ + 47x + 1 is divided by x - 2, then remainder is 7. Find the value of a.

Answer 1

$p(x) = a {x}^{5} - 23 {x}^{3} + 47x + 1 \\ according \: \: to \: \: remainder \: \: theorem \\ p(2) = 7 \\ a \times {2}^{5} - 23 \times {2}^{3} + 47 \times 2 + 1 = 7 \\ 32a = 96 \\ a = 3$