Q. 412 - Intermediate Algebra

Question

In the following exercises, factor completely

$5x^2+5x-60$.

Step-by-Step Solution

Answer

The factors of the given expression are $5(x-3)(x+4)$. 

Step 1. Given and explanation

We have $5x^2+5x-60$.

We can see that this forms a quadratic equation.We know that quadratic equation is of the form

 $x^2+ax+b=(x-c)(x-d)$.

Applying this, we will factorize the given expression.

Step 2. Factorizing the expression.

We have $5x^2+5x-60$.

This can be written as $5(x^2+x+12)$.

Applying the property of quadratic equation,

$$\begin{gathered} 5x^2+5x-60 \\ =5(x^2+x-12) \\ =5(x^2+4x-3x-12) \\ =5\left(x\right(x+4)-3(x+4\left)\right) \\ =5(x+4)(x-3) \end{gathered}$$