Question

Use synthetic division to find the quotient Q and Remainder R when dividing
$\frac{1}{2}{x}^3-\frac{1}{3}{x}^2-\frac{3}{2}x+\frac{1}{3}$ by $x-\frac{1}{2}$

Answer 1

Since the divisor $=x-\frac{1}{2}$

The zero of $x-\frac{1}{2}=0$

$\Rightarrow x=\frac{1}{2}$

$\therefore$ The quotient is $:\frac{1}{2}{x}^2-\frac{1}{12}x-\frac{37}{24}$

$\Rightarrow$ Remainder $=\frac{\left(\frac{-21}{48}\right)}{(x-\frac{1}{2})}.$

Hence, solved.