# Is it possible to factor 3x^2+ 7x + 2? If so, what are the factors?

Feb 28, 2016

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

#### Explanation:

The whole number factors of 3 can only be 1 and 3
The whole number factors of 2 can only be 1 and 2

$3 \times 2 = 6$ which is close to 7 so lets try it!

$\textcolor{b l u e}{\text{Attempt 1}}$

(3x+2)(x+1) = 3x^2+3x+2x+2 =3x^2+color(red)(5x)+2 color(red)(" Fail"

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Attempt 2}}$

$\left(3 x + 1\right) \left(x + 2\right) = 3 {x}^{2} + 6 x + x + 2 = 3 {x}^{2} + 7 x + 2 \textcolor{g r e e n}{\text{ Works!}}$