Question

Match the polynomial expression on the left with the simplified version on the right. Second expression

Answer 1

The expression given is,

$\:\frac{12x^4-5x^3+x^2+10x-8}{3x^2+x-2}$

Simplify

$\begin{gathered} \frac{\left(x+1\right)\left(3x-2\right)\left(4x^2-3x+4\right)}{3x^2+x-2} \\ \frac{\left(x+1\right)\left(3x-2\right)\left(4x^2-3x+4\right)}{\left(3x-2\right)\left(x+1\right)} \\ \mathrm{Cancel\:the\:common\:factor:}\:x+1 \\ \frac{\left(3x-2\right)\left(4x^2-3x+4\right)}{3x-2} \\ \mathrm{Cancel\:the\:common\:factor:}\:3x-2 \\ =4x^2-3x+4 \end{gathered}$

Hence, the answer is

$4x^2-3x+4$