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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)#

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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Answer 2

Ethan Adkins

To find the LCM of (x^2-8x+7) and (x^2+x-2), we need to factorize both expressions.

(x^2-8x+7) can be factored as (x-7)(x-1).

(x^2+x-2) can be factored as (x+2)(x-1).

Next, we identify the common factors between the two expressions, which is (x-1).

To find the LCM, we multiply the highest power of each unique factor. In this case, we have (x-7), (x+2), and (x-1).

Therefore, the LCM of (x^2-8x+7) and (x^2+x-2) is (x-7)(x+2)(x-1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.