Chapter 8.6, Problem 20PPS

To determine

To factor: The polynomial $5x^2+34x+24$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 20PPS

  $\left(x+6\right)\left(5x+4\right)$

Explanation of Solution

Given:

  $5x^2+34x+24$

Calculation:

The given polynomial is $5x^2+34x+24$

Rewrite the middle term as $34x=30x+4x$ . So, the polynomial becomes

  $5x^2+30x+4x+24$

Make group as shown below

  $\left(5x^2+30x\right)+\left(4x+24\right)$

Factor out the GCF from each of the group

  $5x\left(x+6\right)+4\left(x+6\right)$

Finally, factored out the common factor

  $\left(x+6\right)\left(5x+4\right)$

Therefore, the factored form of the given polynomial is $\left(x+6\right)\left(5x+4\right)$