Question

find the remainder when the polynomial p(x)=12x^3-13x^2-5x+7 is divided by g(x)=(2x+3)

Answer 1

$p(x) = 12 {x}^{3} - 13 {x}^{2} - 5x + 7 \\ g(x) = 2x + 3 \\ = > x = - \frac{3}{2} \\ p( - \frac{3}{2} ) = 12 {( - \frac{3}{2} )}^{3} - 13 {( - \frac{3}{2}) }^{2} - 5( - \frac{3}{2} ) + 7 \\ = > - 12( \frac{27}{8} ) - 13( \frac{9}{4} ) + \frac{15}{2} + 7 \\ = > - \frac{324}{8} - \frac{234}{8} + \frac{60}{8} + \frac{56}{8} \\ = > - \frac {558}{8} + \frac{116}{8} \\ = > - \frac{442}{8} \\ = > -55 \frac{1}{4}$