How do you factor x^2+3x+4x+12 by grouping?

Aug 3, 2018

$\left(x + 3\right) \left(x + 4\right)$

Explanation:

${x}^{2} + 3 x + 4 x + 12$

Grouping;

$\left({x}^{2} + 3 x\right) \left(+ 4 x + 12\right)$

Factoring;

$x \left(x + 3\right) + 4 \left(x + 3\right)$

$\left(x + 3\right) \left(x + 4\right)$

Aug 3, 2018

$\left(x + 3\right) \left(x + 4\right)$

Explanation:

Let's look at our quadratic as two parts:

$\textcolor{s t e e l b l u e}{{x}^{2} + 3 x} + \textcolor{p u r p \le}{4 x + 12}$

We see that the blue terms have an $x$ in common, and the purple terms have a $4$ in common, so we can factor that out to get

$\textcolor{s t e e l b l u e}{x \left(x + 3\right)} + \textcolor{p u r p \le}{4 \left(x + 3\right)}$

We now see that both terms have an $x + 3$ in common, so we can finally factor that out to get

$\left(x + 3\right) \left(x + 4\right)$

Hope this helps!