Q. 408 - Intermediate Algebra

Question

In the following exercises, factor completely

$6a^2-25a-9$.

Step-by-Step Solution

Answer

The factors of the given expression are $(3a+1)(2a-9)$. 

Step 1. Given and explanation

We have $6a^2-25a-9$.

We can see that this forms a quadratic equation which is given by

$x^2-ax+b=(x-c)(x-d)$

Step 2. Factorizing the expression.

We can see that this forms a quadratic equation which is given by

$x^2-ax+b=(x-c)(x-d)$

Therefore,

$$\begin{gathered} 6a^2-25a-9 \\ =6a^2-27a+2a-9 \\ =3a(2a-9)+1(2a-9) \\ =(2a-9)(3a+1) \end{gathered}$$