Chapter 8.6, Problem 11PPS

To determine

To factor: The polynomial $x^2+17x+42$ . Confirm your answer using a graphing calculator.

Answer to Problem 11PPS

  $\left(x+14\right)\left(x+3\right)$

Explanation of Solution

Given:

  $x^2+17x+42$

Calculation:

The given polynomial is $x^2+17x+42$

Rewrite the middle term as $17x=14x+3x$ . So, the polynomial becomes

  $x^2+14x+3x+42$

Make group as shown below

  $\left(x^2+14x\right)+\left(3x+42\right)$

Factor out the GCF from each of the group

  $x\left(x+14\right)+3\left(x+14\right)$

Finally, factored out the common factor

  $\left(x+14\right)\left(x+3\right)$

Therefore, the factored form of the given polynomial is $\left(x+14\right)\left(x+3\right)$

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

  $\left(x+14\right)\left(x+3\right)$

So, the answer is verified.