Question

Factor each polynomial.

$\mathbf{3}{x}^2+\mathbf{6}x+x+\mathbf{2}$

Short answer

The factors of given polynomial are $\left(\mathbf{3}x+\mathbf{1}\right)\left(x+\mathbf{2}\right)$.

Step-by-step solution

Step 1. Combine.

Combine like terms in the given polynomial.

$3x^2+7x+2$

Step 2. Find the GCF.

Find the GCF of$3x^2,7x$ and 2.

$$\begin{gathered} 3x^2=1\cdot 3\cdot x\cdot x \\ 7x=1\cdot 7\cdot x \\ 2=1\cdot 2 \end{gathered}$$

Therefore, GCF is 1.

Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 6 and sum of 7. The numbers are 1 and 6.

$3x^2+mx+nx+2=3x^2+6x+1x+2$

Step 4. Group terms with common factors and factor out GCF.

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

$$\begin{gathered} \left(3x^2+6x\right)+\left(1x+2\right)=3x\left(x+2\right)+1\left(x+2\right) \\ =\left(3x+1\right)\left(x+2\right) \end{gathered}$$

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