How do you factor x^2 + 2x + 4x + 8 by grouping?

May 15, 2016

${x}^{2} + 2 x + 4 x + 8 = \left(x + 4\right) \left(x + 2\right)$

Explanation:

Group the terms using parentheses:

$\left({x}^{2} + 2 x\right) + \left(4 x + 8\right)$

Identify the common factor inside each pair of parentheses and separate it out:

$x \left(x + 2\right) + 4 \left(x + 2\right)$

Combine the coefficients of the common factor:

$\left(x + 4\right) \left(x + 2\right)$

I would normally simply write this:

${x}^{2} + 2 x + 4 x + 8$

$= \left({x}^{2} + 2 x\right) + \left(4 x + 8\right)$

$= x \left(x + 2\right) + 4 \left(x + 2\right)$

$= \left(x + 4\right) \left(x + 2\right)$