Chapter 8.6, Problem 32PPS

To determine

To factor: The polynomial $x^2-14xy-51y^2$

Answer to Problem 32PPS

  $\left(x-17y\right)\left(x+3y\right)$

Explanation of Solution

Given:

  $x^2-14xy-51y^2$

Calculation:

The given polynomial is $x^2-14xy-51y^2$

Rewrite the middle term as $14xy=-17xy+3xy$ . So, the polynomial becomes

  $x^2-17xy+3xy-51y^2$

Make group as shown below

  $\left(x^2-17xy\right)+\left(3xy-51y^2\right)$

Factor out the GCF from each of the group

  $x\left(x-17y\right)+3y\left(x-17y\right)$

Finally, factored out the common factor

  $\left(x-17y\right)\left(x+3y\right)$

Therefore, the factored form of the given polynomial is $\left(x-17y\right)\left(x+3y\right)$