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

1 Answer

Nov 1, 2017

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

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 $=(x-7)(x-1)(x+2)$

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

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

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