Question

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

Answer 1

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^2-8x+7)color(white)("xxxxxx")underbrace(x^2+x-2)`
`(x-7)(x-1)color(white)("xxx")(x+2)(x-1)`

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

LCM `=(x-7)(x-1)(x+2)`

`color(white)("XXX")=(x^2-8x+7)(x+2)`

`color(white)("XXX")=x^3-8x^2+7x`
`color(white)("XXX")ul(color(white)(=x^3-)2x^2-16x+14)`
`color(white)("XXX")=x^3-6x^2-9x+14`