Chapter 8.6, Problem 2AGP

To determine

To factor: The polynomial $21-22m+m^2$

Answer to Problem 2AGP

  $\left(m-21\right)\left(m-1\right)$

Explanation of Solution

Given:

  $21-22m+m^2$

Calculation:

The given polynomial is $21-22m+m^2$

Write the polynomial in standard form

  $m^2-22m+21$

Rewrite the middle term as $-22m=-21m-m$ . So, the polynomial becomes

  $m^2-21m-m+21$

Make group as shown below

  $\left(m^2-21m\right)+\left(-m+21\right)$

Factor out the GCF from each of the group

  $m\left(m-21\right)-1\left(m-21\right)$

Finally, factored out the common factor

  $\left(m-21\right)\left(m-1\right)$

Therefore, the factored form of the given polynomial is $\left(m-21\right)\left(m-1\right)$