Question

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

Answer 1

The expression given is,

`\:(12x^4-5x^3+x^2+10x-8)/(3x^2+x-2)`

Simplify

`\begin{gathered} (\left(x+1\right)\left(3x-2\right)\left(4x^2-3x+4\right))/(3x^2+x-2) \\ (\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 \\ (\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`