Chapter 8.6, Problem 38PPS

To determine

To factor: The polynomial $-4x^2-15x-14$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 38PPS

  $-\left(x+2\right)\left(4x+7\right)$

Explanation of Solution

Given:

  $-4x^2-15x-14$

Calculation:

The given polynomial is $-4x^2-15x-14$

Rewrite this polynomial as

  $-\left(4x^2+15x+14\right)$

Rewrite the middle term as $15x=8x+7x$ . So, the polynomial becomes

  $-\left(4x^2+8x+7x+14\right)$

Make group as shown below

  $-\left(\left(4x^2+8x\right)+\left(7x+14\right)\right)$

Factor out the GCF from each of the group

  $-\left(4x\left(x+2\right)+7\left(x+2\right)\right)$

Finally, factored out the common factor

  $-\left(x+2\right)\left(4x+7\right)$

Therefore, the factored form of the given polynomial is $-\left(x+2\right)\left(4x+7\right)$