# How do you factor (x+2)^2-7(x+2)+12?

Nov 10, 2015

$\left(x - 1\right) \left(x - 2\right)$

#### Explanation:

Expand all the terms:

$\left({x}^{2} + 4 x + 4\right) - \left(7 x - 14\right) + 12 = {x}^{2} - 3 x + 2$

Solve the quadratic equation: when dealing with a quadratic $a {x}^{2} + b x + c$, we know that the two solutions are given by the formula

${x}_{1 , 2} = \setminus \frac{- b \setminus \pm \setminus \sqrt{{b}^{2} - 4 a c}}{2 a}$

Plugging the values,

${x}_{1 , 2} = \setminus \frac{3 \setminus \pm \setminus \sqrt{9 - 8}}{2} = \setminus \frac{3 \setminus \pm 1}{2}$

Which means that ${x}_{1} = 1$ and ${x}_{2} = 2$.

When you find the solutions of a quadratic equation, if $a = 1$, you can write

${x}^{2} + b x + c = \left(x - {x}_{1}\right) \left(x - {x}_{2}\right)$, so in your case

${x}^{2} - 3 x + 2 = \left(x - 1\right) \left(x - 2\right)$