Chapter 4.3, Problem 8CYU

To determine

To calculate: The factors of the polynomial $2x^2+7x-30$ .

Answer to Problem 8CYU

The polynomial is factored as $\left(x+6\right)\left(2x-5\right)$ .

Explanation of Solution

Given information:

The polynomial $2x^2+7x-30$ .

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 $2x^2+7x-30$ .

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 $12$ and $-5$ are two numbers such that their sum is $7$ and product is $-60$ .

Apply it, first the group the similar terms,

  $\begin{array}{c}2x^2+7x-30=2x^2+12x-5x-30\\ =2x\left(x+6\right)-5\left(x+6\right)\\ =\left(x+6\right)\left(2x-5\right)\end{array}$

Thus, the polynomial is factored as $\left(x+6\right)\left(2x-5\right)$ .