Question

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

Short answer

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

Step-by-step solution

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 role="math" localid="1644821512753" $-24$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 $\left(2n-1\right)\left(3n+4\right)$

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