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# x^3-8 How to change this to (x-2)(x^2+2x+4) ?

how does this get changed in to (x-2)(x^2+2x+4)  ?

### 2 Answers by Expert Tutors

4.9 4.9 (233 lesson ratings) (233)
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Hey Jo -- we may notice x=2 is a root of X*X*X =8 ... next divide x^3-8 by (x-2)
=> x^2 +2x +4 ... factors are thus (x-2)(x^2 +2x +4) ... Best wishes :)
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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This is the difference of two cubes.  It is similar to a difference of two squares in that there is a formula for factoring it.

This is the formula
(a3 - b3) = (a2 +ab + b2)
In this case a = x since (x)3 = xand b = 2, since 23 = 8.

So plug in x for a, and 2 for b into the following:
(a3 - b3) = (a2 +ab + b2)

Giving you:
(x3 - 8) = (x-2)(x2 + (x)(2) + 22) = (x-2)(x2 + 2x + 4)

Check

x(x2 +2x + 4) - 2(x2 + 2x + 4)

x3 +2x2 +4x -2x2 -4x - 8

The x2 terms and the x terms cancel out and you are left with:

x3 - 8

Note that if it had been x3 + 8, the factors would be (x+2)(x2-2x+4)