# How do you factor 3x^2+4x+1??

Dec 9, 2015

$3 {x}^{2} + 4 x + 1 = \left(3 x + 1\right) \left(x + 1\right)$

#### Explanation:

$3 {x}^{2} + 4 x + 1$ is a quadratic equation in the form $a {x}^{2} + b x + c$, where $a = 3 , b = 4 , \mathmr{and} c = 1$.

Use the AC method to factor the equation.

Multiply $a$ times $c$.

$3 \times 1 = 3$

Find two numbers that when added equal $4$ and when multiplied equal $3$. The numbers are $3$ and $1$.

Rewrite the equation, substituting the middle term (b) with $3 x$ and $x$.

$3 {x}^{2} + 3 x + x + 1$

Group the terms into two groups.

$\left(3 {x}^{x} + 3 x\right) + \left(x + 1\right)$

Factor $3 x$ out of the first group.

$3 x \left(x + 1\right) + \left(x + 1\right)$

Factor out $\left(x + 1\right)$

$\left(3 x + 1\right) \left(x + 1\right)$