Chapter 8.6, Problem 15PPS

To determine

To factor: The polynomial $44+15h+h^2$ . Confirm your answer using a graphing calculator.

Answer to Problem 15PPS

  $\left(h+11\right)\left(h+4\right)$

Explanation of Solution

Given:

  $44+15h+h^2$

Calculation:

The given polynomial is $44+15h+h^2$

Write this is standard form

  $h^2+15h+44$

Rewrite the middle term as $15h=11h+4h$ . So, the polynomial becomes

  $h^2+11h+4h+44$

Make group as shown below

  $\left(h^2+11h\right)+\left(4h+44\right)$

Factor out the GCF from each of the group

  $h\left(h+11\right)+4\left(h+11\right)$

Finally, factored out the common factor

  $\left(h+11\right)\left(h+4\right)$

Therefore, the factored form of the given polynomial is $\left(h+11\right)\left(h+4\right)$

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

  $\left(h+11\right)\left(h+4\right)$

So, the answer is verified.