Chapter 8.5, Problem 40PPS

To determine

To factor: The polynomial $4bc-10b+5c-2c^2$

Answer to Problem 40PPS

  $\left(2c-5\right)\left(2b-c\right)$

Explanation of Solution

Given:

  $4bc-10b+5c-2c^2$

Calculation:

The given polynomial is $4bc-10b+5c-2c^2$

Make groups as shown below

  $\left(4bc-10b\right)+\left(5c-2c^2\right)$

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

  $\begin{array}{l}\left(4bc-10b\right)+\left(5c-2c^2\right)\\ =2b\left(2c-5\right)-c\left(2c-5\right)\\ =\left(2c-5\right)\left(2b-c\right)\end{array}$

So, the factored form is $\left(2c-5\right)\left(2b-c\right)$