Question

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

Answer 1

Given the following question:

First expression:

`\begin{gathered} (12x^3-14x^2+16x-8)/(3x-2) \\ \text{ Factor the expression:} \\ 12x^3-14x^2+16x-8=2(6x^3-7x^2+8x-4) \\ (2\left(6x^3-7x^2+8x-4\right))/(3x-2) \\ \text{ Factor:} \\ 2\left(6x^3-7x^2+8x-4\right)=(3x-2)(2x^2-x+2) \\ =(3x-2)(2x^2-x+2)=2\left(3x-2\right)\left(2x^2-x+2\right) \\ (2\left(3x-2\right)\left(2x^2-x+2\right))/(3x-2) \\ \text{ Cancel the common factor:} \\ -(3x-2) \\ 4x^2-2x+4 \end{gathered}`

Second expression: