Question

using remainder theorem find the remainder when the polynomial p(x)=2x²-6x³+2x²-x+2 is divided by x+2

Answer 1

$p(x) = 2x {}^{2} - 6x {}^{3} + 2x {}^{2} - x + 2 \\ = - 6x {}^{3} + 4x {}^{2} - x + 2 \\ g(x) = x + 2$
$by \: remainder \: theorem \\ x + 2 = 0 \\ x = - 2$
$so \: \: remainer \: = p( - 2)$
$= - 6 \times ( - 2) {}^{3} + 4 \times ( - 2) {}^{2} - ( - 2) + 2 \\ = 48 + 16 + 2 + 2 \\ = 68$
So,remainder left is 48.