Chapter 8.5, Problem 5P

To determine

To factor: the polynomial $m^2+6mn-27n^2$ .

Answer to Problem 5P

The factor of polynomial is $\left(m-9n\right)\left(m+3n\right)$ .

Explanation of Solution

Given:

The polynomial is $m^2+6mn-27n^2$ .

Calculation:

The factor of polynomial as follows:

  $\begin{array}{l}\Rightarrow m^2+6mn-27n^2\\ \Rightarrow m^2-9mn+3mn-27n^2\left(-27n^2{m}^2=\left(-9mn\right)\left(3mn\right)\right)\\ \Rightarrow m\left(m-9n\right)+3n\left(m-9n\right)\\ \Rightarrow \left(m-9n\right)\left(m+3n\right)\end{array}$

Thus, the factor of polynomial is $\left(m-9n\right)\left(m+3n\right)$ .