# How do you find the LCM of (x^2-8x+7),(x^2+x-2)?

Nov 1, 2017

LCM(x^2-8x+7, x^2+x-2)=color(red)(x^3-6x^2-9x+14)

#### Explanation:

Factoring the two given polynomials:
$\underbrace{{x}^{2} - 8 x + 7} \textcolor{w h i t e}{\text{xxxxxx}} \underbrace{{x}^{2} + x - 2}$
$\left(x - 7\right) \left(x - 1\right) \textcolor{w h i t e}{\text{xxx}} \left(x + 2\right) \left(x - 1\right)$

We notice the duplicate factor $\left(x - 1\right)$, so one copy of this can be eliminated.

LCM $= \left(x - 7\right) \left(x - 1\right) \left(x + 2\right)$

$\textcolor{w h i t e}{\text{XXX}} = \left({x}^{2} - 8 x + 7\right) \left(x + 2\right)$

$\textcolor{w h i t e}{\text{XXX}} = {x}^{3} - 8 {x}^{2} + 7 x$
$\textcolor{w h i t e}{\text{XXX}} \underline{\textcolor{w h i t e}{= {x}^{3} -} 2 {x}^{2} - 16 x + 14}$
$\textcolor{w h i t e}{\text{XXX}} = {x}^{3} - 6 {x}^{2} - 9 x + 14$