Chapter 8.6, Problem 22PPS

To determine

To factor: The polynomial $4x^2+38x+70$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 22PPS

  $2\left(x+7\right)\left(2x+5\right)$

Explanation of Solution

Given:

  $4x^2+38x+70$

Calculation:

The given polynomial is $4x^2+38x+70$

Factored out the GCF

  $2\left(2x^2+19x+35\right)$

Rewrite the middle term as $19x=14x+5x$ . So, the polynomial becomes

  $2\left(2x^2+14x+5x+35\right)$

Make group as shown below

  $2\left(\left(2x^2+14x\right)+\left(5x+35\right)\right)$

Factor out the GCF from each of the group

  $2\left(2x\left(x+7\right)+5\left(x+7\right)\right)$

Finally, factored out the common factor

  $2\left(x+7\right)\left(2x+5\right)$

Therefore, the factored form of the given polynomial is $2\left(x+7\right)\left(2x+5\right)$