Chapter 4.3, Problem 28PPS

To determine

To calculate: The factors of the polynomial $3x^2+12x-36$ .

Answer to Problem 28PPS

The polynomial is factored as $3\left(x+6\right)\left(x-2\right)$ .

Explanation of Solution

Given information:

The polynomial $3x^2+12x-36$ .

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 $3x^2+12x-36$ .

Take out the common factor,

  $3x^2+12x-36=3\left(x^2+4x-12\right)$

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 $-2$ are two numbers such that their sum is $4$ and product is $-12$ .

Apply it, first the group the similar terms,

  $\begin{array}{c}3x^2+12x-36=3\left(x^2+4x-12\right)\\ =3\left(x^2+6x-2x-12\right)\\ =3\left[x\left(x+6\right)-2\left(x+6\right)\right]\\ =3\left(x+6\right)\left(x-2\right)\end{array}$

Thus, the polynomial is factored as $3\left(x+6\right)\left(x-2\right)$ .