Chapter 4.5, Problem 24WE

To determine

To factor: the provided polynomial

Answer to Problem 24WE

The factor of the provided polynomial is $\left(v-1\right)\left(u-2\right)$

Explanation of Solution

Given information: the polynomial provided in the question,

  $u\left(v-1\right)-2\left(1-v\right)$

Calculation:

Change the sign of the second parenthesis to make it same as the first parenthesis,

  $\begin{array}{l}u\left(v-1\right)-2\left(1-v\right)\\ =u\left(v-1\right)+2\left(v-1\right)\end{array}$

Factor the common factor and the rest inside the parenthesis,

  $\begin{array}{l}u\left(v-1\right)-2\left(v-1\right)\\ =\left(v-1\right)\left(u-2\right)\end{array}$

Hence, the factor of the provided polynomial is $\left(v-1\right)\left(u-2\right)$