Q. 141E - Intermediate Algebra

Question

In the following exercises, factor each expression using any method. $6n^2+5n-4$

Step-by-Step Solution

Answer

The factors are $\left(2n-1\right)\left(3n+4\right)$

Step 1. Given Information

The trinomial is $6n^2+5n-4$ .

Find factors using 'ac' method .

Step 2. Find 'ac'

Compare the trinomial to $a{x}^2+bx+c$and find product 'ac'

$6n^2+5n-4$ So, $a=6, b=5, c=-4$

Hence $ac=-24$

Find two numbers such as product is $-24$ and sum is 5

So, the numbers are $8, -3$

Step 3. Factor the trinomial

Split the middle term of trinomial to find factors 

$6n^2-3n+8n-4$

Factor it

$$\begin{gathered} 3n\left(2n-1\right)+4\left(2n-1\right) \\ \left(2n-1\right)\left(3n+4\right) \end{gathered}$$

Step 4. Check

Multiply the factors $\left(2n-1\right)\left(3n+4\right)$

$$\begin{gathered} 6n^2-3n+8n-4 \\ 6n^2+5n-4 \end{gathered}$$