How do you factor completely #5x^2 − 40#?

1 Answer
Jim H
Oct 1, 2017

Please see below.

Explanation:

If we are to use integers only, we factor it as

#5x^2-40 = 5(x^2-8)#

Since #sqrt8 = 2sqrt2# is irrational, we do not continue unless we are fartoring using all real numbers. If we are allowed to use any real number, we factor it as

#5x^2-40 = 5(x^2-8) = 5(x+sqrt8)(x-sqrt8) = 5(x+2sqrt2)(x-2sqrt2)#

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