Question

Factor each polynomial.

$6x^2-5x-4$

Short answer

The factors of given polynomial are $\left(3x-4\right)\left(2x+1\right)$.

Step-by-step solution

Step 1. Find the GCF.

Find the GCF of $6x^2,5x$and 4.

$$\begin{gathered} 6x^2=1\cdot 2\cdot 3\cdot x\cdot x \\ 6x^2=1\cdot 2\cdot 3\cdot x\cdot x \\ 4=1\cdot 2\cdot 2 \end{gathered}$$

Therefore, GCF is 1.

Step 2. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 24 and sum of $-5$. The numbers are$3$ and $-8$.

$6x^2+mx+nx-4=6x^2+3x-8x-4$

Step 3. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

$\begin{array}{c}\left(6x^2+3x\right)+\left(-8x-4\right)=3x\left(2x+1\right)-4\left(2x+1\right)\\ =\left(3x-4\right)\left(2x+1\right)\end{array}$

Therefore, the factors of$6x^2-5x-4$ are $\left(3x-4\right)\left(2x+1\right)$.