Chapter 14.8, Problem 1AGP

To determine

To calculate: The factors of the trinomial $x^2+7x+10$ .

Answer to Problem 1AGP

The factors of the trinomial $x^2+7x+10$ are $x+2\text{and}x+5$ .

Explanation of Solution

Given Information:

The trinomial expressionis $x^2+7x+10$ .

Calculation:

The given trinomial is $x^2+7x+10$ .

Find the factors of the trinomial.

Split $7x$ into two parts such that their product is equal to the product of $x^2$ and 10.

  $\begin{array}{c}{x}^2+7x+10=x^2+5x+2x+10\\ =x\left(x+5\right)+2\left(x+5\right)\\ =\left(x+2\right)\left(x+5\right)\end{array}$

Hence, the factors of the trinomial $x^2+7x+10$ are $x+2\text{and}x+5$ .