Chapter 8.5, Problem 11CYU

To determine

To factor: The polynomial $10p^{3}q-5p^4+3pq-6q^2$

Answer to Problem 11CYU

  $\left(2q-p\right)\left(5p^3-3q\right)$

Explanation of Solution

Given:

  $10p^{3}q-5p^4+3pq-6q^2$

Calculation:

The given polynomial is $10p^{3}q-5p^4+3pq-6q^2$

Make groups as shown below

  $\left(10p^{3}q-5p^4\right)+\left(3pq-6q^2\right)$

So, factored out the GCF from each of the group and then factored out the common factor

  $\begin{array}{l}\left(10p^{3}q-5p^4\right)+\left(3pq-6q^2\right)\\ =5p^3\left(2q-p\right)-3q\left(-p+2q\right)\\ =\left(2q-p\right)\left(5p^3-3q\right)\end{array}$

So, the factored form is $\left(2q-p\right)\left(5p^3-3q\right)$