Chapter 14.8, Problem 17PPS

To determine

To calculate: The factors of the trinomial $x^2+24x+95$ .

Answer to Problem 17PPS

The factors of the trinomial $x^2+24x+95$ are $x+19\text{and}x+5$ .

Explanation of Solution

Given Information:

The trinomial expressionis $x^2+24x+95$ .

Calculation:

The given trinomial is $x^2+24x+95$ .

Split $24x$ into two parts such that their product is equal to the product of $x^2$ and $95$ .

  $\begin{array}{c}{x}^2+24x+95=x^2+5x+19x+95\\ =x\left(x+5\right)+19\left(x+5\right)\\ =\left(x+5\right)\left(x+19\right)\end{array}$

Hence, the factors of the trinomial $x^2+24x+95$ are $x+19\text{and}x+5$ .