# How do you use synthetic division to divide (2x^3-x^2+5x-12) /(2x - 3) ?

Mar 28, 2018

Quotient is ${x}^{2} + x + 4$ and remainder is $0$.

#### Explanation:

$2 {x}^{3} - {x}^{2} + 5 x - 12$

=$2 {x}^{3} - 3 {x}^{2} + 2 {x}^{2} - 3 x + 8 x - 12$

=${x}^{2} \cdot \left(2 x - 3\right) + x \cdot \left(2 x - 3\right) + 4 \cdot \left(2 x - 3\right)$

=$\left(2 x - 3\right) \cdot \left({x}^{2} + x + 4\right)$

Hence quotient is ${x}^{2} + x + 4$ and remainder is $0$.