Chapter 8.6, Problem 37PPS

To determine

To factor: The polynomial $-6x^2-23x-20$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 37PPS

  $-\left(2x+5\right)\left(3x+4\right)$

Explanation of Solution

Given:

  $-6x^2-23x-20$

Calculation:

The given polynomial is $-6x^2-23x-20$

Rewrite this polynomial as

  $-\left(6x^2+23x+20\right)$

Rewrite the middle term as $23x=15x+8x$ . So, the polynomial becomes

  $-\left(6x^2+15x+8x+20\right)$

Make group as shown below

  $-\left(\left(6x^2+15x\right)+\left(8x+20\right)\right)$

Factor out the GCF from each of the group

  $-\left(3x\left(2x+5\right)+4\left(2x+5\right)\right)$

Finally, factored out the common factor

  $-\left(2x+5\right)\left(3x+4\right)$

Therefore, the factored form of the given polynomial is $-\left(2x+5\right)\left(3x+4\right)$