Chapter 8.6, Problem 5AGP

To determine

To factor: The polynomial $2n^2-n-1$

Answer to Problem 5AGP

  $\left(n-1\right)\left(2n+1\right)$

Explanation of Solution

Given:

  $2n^2-n-1$

Calculation:

The given polynomial is $2n^2-n-1$

Rewrite the middle term as $-n=-2n+n$ . So, the polynomial becomes

  $2n^2-2n+n-1$

Make group as shown below

  $\left(2n^2-2n\right)+\left(n-1\right)$

Factor out the GCF from each of the group

  $2n\left(n-1\right)+1\left(n-1\right)$

Finally, factored out the common factor

  $\left(n-1\right)\left(2n+1\right)$

Therefore, the factored form of the given polynomial is $\left(n-1\right)\left(2n+1\right)$