# How do you factor  3x^2+7x+2?

Jul 11, 2016

$3 {x}^{2} + 7 x + 2 = \left(x + 2\right) \left(3 x + 1\right)$

#### Explanation:

$3 {x}^{2} + 7 x + 2 = \left(x + 2\right) \left(3 x + 1\right)$

Jul 11, 2016

$\left(3 x + 1\right) \left(x + 2\right)$

#### Explanation:

Both 3 and 2 are prime numbers, so there are not many options..

We need the factors of 3 and 2 which add together to make 7.
All the signsare positive.

$3 = 3 \times 1 \mathmr{and} 2 = 2 \times 1$
The only possible combinations are:

$3 \times 1 + 1 \times 2 = 3 + 2 = 5 \text{ wrong combination}$
$3 \times 2 + 1 \times 1 = 6 + 1 = 7 \text{ right combination}$

Choose factors and cross multiply to get 7.

$\text{ 3 1} \Rightarrow 1 \times 1 = 1$
$\text{ 1 2} \Rightarrow 3 \times 2 = 6$ 6+1 = 7

The top row is the one bracket.
The bottom row is the other bracket.
$\left(3 x + 1\right) \left(x + 2\right)$

Verify that these are correct by multiplying out the brackets.