Chapter 4.3, Problem 12CYU

To determine

To calculate: The factors of the polynomial $12x^2-2x-2$ .

Answer to Problem 12CYU

The polynomial is factored as $2\left(2x-1\right)\left(3x+1\right)$ .

Explanation of Solution

Given information:

The polynomial $12x^2-2x-2$ .

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial $12x^2-2x-2$ .

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial $-6$ and $4$ are two numbers such that their sum is $-2$ and product is $-24$ .

Apply it, first the group the similar terms,

  $\begin{array}{c}12x^2-2x-2=12x^2-6x+4x-2\\ =6x\left(2x-1\right)+2\left(2x-1\right)\\ =\left(2x-1\right)\left(6x+2\right)\\ =2\left(2x-1\right)\left(3x+1\right)\end{array}$

Thus, the polynomial is factored as $2\left(2x-1\right)\left(3x+1\right)$ .