# How do you use polynomial synthetic division to divide (2x^3-3x+1)div(x-1/2) and write the polynomial in the form p(x)=d(x)q(x)+r(x)?

$2 {x}^{3} - 3 x + 1 = \left(x - \frac{1}{2}\right) \left(2 {x}^{2} + x - \frac{5}{2}\right) - \left(\frac{1}{4}\right)$