Chapter 8.6, Problem 42PPS

To determine

To factor: The polynomial $-12x^2+x+20$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 42PPS

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

Explanation of Solution

Given:

  $-12x^2+x+20$

Calculation:

The given polynomial is $-12x^2+x+20$

Rewrite this polynomial as

  $-\left(12x^2-x-20\right)$

Rewrite the middle term as $-x=-16x+15x$ . So, the polynomial becomes

  $-\left(12x^2-16x+15x-20\right)$

Make group as shown below

  $-\left(\left(12x^2-16x\right)+\left(15x-20\right)\right)$

Factor out the GCF from each of the group

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

Finally, factored out the common factor

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

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