# What is the factors for (3x² + 4x + 1)?

May 1, 2015

Check for integer solutions first:
Can we find pairs one from each of the sets of factors for 3 and 1 such that the sum of the products of the pairs equals 4?

$3 = \textcolor{red}{3} \times \textcolor{red}{1}$
$1 = \textcolor{b l u e}{1} \times \textcolor{b l u e}{1}$
$\left(\textcolor{red}{3} \times \textcolor{b l u e}{1}\right) + \left(\textcolor{red}{1} \times \textcolor{b l u e}{1}\right) = 4$

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

$= \left(\textcolor{red}{3} x + \textcolor{b l u e}{1}\right) \cdot \left(\textcolor{red}{1} x + \textcolor{b l u e}{1}\right)$