Chapter 8.5, Problem 54HP

To determine

To write: A four term polynomial that can be factored from the grouping. Then factor the polynomial.

Answer to Problem 54HP

The four term polynomial is $4x{y}^2+24y+5xy+30$

Its factored form is $\left(xy+6\right)\left(4y+5\right)$

Explanation of Solution

Given:

Four term polynomial

Calculation:

Let the four term polynomial is $4x{y}^2+24y+5xy+30$

Make group as shown below

  $\left(4x{y}^2+24y\right)+\left(5xy+30\right)$

Factored out the GCF from each group

  $4y\left(xy+6\right)+5\left(xy+6\right)$

Factored out the common factor

  $\left(xy+6\right)\left(4y+5\right)$