Chapter 8.5, Problem 60PFA

To determine

To find: The factor of the expression $6b^{2}c-9bc+22bd-33d$

Answer to Problem 60PFA

  $\left(3bc+11d\right)\left(2b-3\right)$

B is the correct option.

Explanation of Solution

Given:

Options are

  $\begin{array}{l}\mathrm{A }\left(3bc+11d\right){\left(2b-3\right)}^2\\ \mathrm{B }\left(3bc+11d\right)\left(2b-3\right)\\ \mathrm{C }\left(2b-3\right)\\ \mathrm{D }\left(3bc-11d\right)\left(2b+3\right)\end{array}$

Calculation:

The given expression is $6b^{2}c-9bc+22bd-33d$

Make group as shown below

  $\left(6b^{2}c-9bc\right)+\left(22bd-33d\right)$

Factor out GCF from each group

  $3bc\left(2b-3\right)+11d\left(2b-3\right)$

Now, factored out the common term

  $\left(3bc+11d\right)\left(2b-3\right)$

Hence, B is the correct option.