Chapter 8.6, Problem 3CYU

To determine

To factor: The polynomial $n^2+4n-21$ . Confirm your answer using a graphing calculator.

Answer to Problem 3CYU

  $\left(n+7\right)\left(n-3\right)$

Explanation of Solution

Given:

  $n^2+4n-21$

Calculation:

The given polynomial is $n^2+4n-21$

Rewrite the middle term as $4n=7n-3n$ . So, the polynomial becomes

  $n^2+7n-3n-21$

Make group as shown below

  $\left(n^2+7n\right)+\left(-3n-21\right)$

Factor out the GCF from each of the group

  $n\left(n+7\right)-3\left(n+7\right)$

Finally, factored out the common factor

  $\left(n+7\right)\left(n-3\right)$

Therefore, the factored form of the given polynomial is $\left(n+7\right)\left(n-3\right)$

Now, using a graphing calculator, the factor of the polynomial is given by

  $\left(n+7\right)\left(n-3\right)$

So, the answer is verified.