Chapter 8.6, Problem 10CYU

To determine

To factor: The polynomial $3x^2-11x-20$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 10CYU

  $\left(x+5\right)\left(3x+4\right)$

Explanation of Solution

Given:

  $3x^2-11x-20$

Calculation:

The given polynomial is $3x^2-11x-20$

Rewrite the middle term as $-11x=-15x+4x$ . So, the polynomial becomes

  $3x^2-15x+4x-20$

Make group as shown below

  $\left(3x^2-15x\right)+\left(4x-20\right)$

Factor out the GCF from each of the group

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

Finally, factored out the common factor

  $\left(x+5\right)\left(3x+4\right)$

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