# How do you factor completely x^2+2x+3x+6?

Dec 16, 2015

Factor by grouping to find:

${x}^{2} + 2 x + 3 x + 6 = \left(x + 3\right) \left(x + 2\right)$

#### Explanation:

Factor by grouping as follows:

${x}^{2} + 2 x + 3 x + 6$

$= \left({x}^{2} + 2 x\right) + \left(3 x + 6\right)$

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

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

With this question, the hard/fun part has already been done for you, viz splitting the $x$ term into $2 x + 3 x$. Normally you would be given something like ${x}^{2} + 5 x + 6$ and have to find the split yourself.

If you did have to find the split yourself, you would look for two numbers which add up to $5$ and multiply together to give $6$.

Notice that in general, $\left(x + a\right) \left(x + b\right) = {x}^{2} + \left(a + b\right) x + a b$