Question

webwork / hs rowe cpma / 6.4 trinomials where a does not
6.4 trinomials where a does
(1 point)
factor:
$5x^2 + 5x - 60 = \square$
you have attempted this problem 0 times.
you have unlimited attempts remaining.

Explanation:

Step1: Factor out the greatest common factor

The greatest common factor of \(5x^{2}\), \(5x\), and \(-60\) is \(5\).

$$5x^{2}+5x - 60=5(x^{2}+x - 12)$$

Step2: Factor the quadratic trinomial \(x^{2}+x - 12\)

We need to find two numbers \(m\) and \(n\) such that \(m + n=1\) (the coefficient of \(x\)) and \(m\times n=- 12\) (the constant term). The numbers are \(4\) and \(-3\) since \(4+( - 3)=1\) and \(4\times(-3)=-12\).

$$x^{2}+x - 12=(x + 4)(x-3)$$

Answer:

\(5(x + 4)(x - 3)\)