Chapter 8.5, Problem 44PPS

To determine

To factor: The polynomial $2a^{3}b-8a^2+12b-3a{b}^2$

Answer to Problem 44PPS

  $\left(ab-4\right)\left(2a^2-3b\right)$

Explanation of Solution

Given:

  $2a^{3}b-8a^2+12b-3a{b}^2$

Calculation:

The given polynomial is $2a^{3}b-8a^2+12b-3a{b}^2$

Make groups as shown below

  $\left(2a^{3}b-8a^2\right)+\left(12b-3a{b}^2\right)$

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

  $\begin{array}{l}\left(2a^{3}b-8a^2\right)+\left(12b-3a{b}^2\right)\\ =2a^2\left(ab-4\right)-3b\left(ab-4\right)\\ =\left(ab-4\right)\left(2a^2-3b\right)\end{array}$

So, the factored form is $\left(ab-4\right)\left(2a^2-3b\right)$