Chapter 14, Problem 35PT

To determine

To calculate: Check whether the polynomial $y^2-16y-36$ can be factored or not.

Answer to Problem 35PT

The factors of the polynomial expression $y^2-16y-36$ are $y-18\text{and}y+2$ .

Explanation of Solution

Given Information:

The polynomial expression is $y^2-16y-36$ .

Calculation:

The given polynomial expression is $y^2-16y-36$ .

Split the term $-16y$ into two parts such that their product is equal to the product of $-36$ and $y^2$ .

  $\begin{array}{c}{y}^2-16y-36=y^2-18y+2y-36\\ =y\left(y-18\right)+2\left(y-18\right)\\ =\left(y-18\right)\left(y+2\right)\end{array}$

Hence, thefactors of the polynomial expression $y^2-16y-36$ are $y-18\text{and}y+2$ .