Chapter 8.6, Problem 39PPS

To determine

To factor: The polynomial $-5x^2+18x+8$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 39PPS

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

Explanation of Solution

Given:

  $-5x^2+18x+8$

Calculation:

The given polynomial is $-5x^2+18x+8$

Rewrite this polynomial as

  $-\left(5x^2-18x-8\right)$

Rewrite the middle term as $-18x=-20x+2x$ . So, the polynomial becomes

  $-\left(5x^2-20x+2x-8\right)$

Make group as shown below

  $-\left(\left(5x^2-20x\right)+\left(2x-8\right)\right)$

Factor out the GCF from each of the group

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

Finally, factored out the common factor

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

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