Chapter 8.6, Problem 27PPS

To determine

To factor: The polynomial $12x^2+69x+45$ , if possible. If the polynomial cannot be factored using integers write prime.

Answer to Problem 27PPS

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

Explanation of Solution

Given:

  $12x^2+69x+45$

Calculation:

The given polynomial is $12x^2+69x+45$

Factored out the GCF

  $3\left(4x^2+23x+15\right)$

Rewrite the middle term as $23x=20x+3x$ . So, the polynomial becomes

  $3\left(4x^2+20x+3x+15\right)$

Make group as shown below

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

Factor out the GCF from each of the group

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

Finally, factored out the common factor

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

Therefore, the factored form of the given polynomial is

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