**x=2 is a root**of X*X*X =8 ...

**next divide**x^3-8

**by (x-2)**

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

Tutors, sign in to answer this question.

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 :)

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

(a^{3} - b^{3}) = (a^{2} +ab + b^{2})

In this case a = x since (x)^{3} = x^{3 }and b = 2, since 2^{3} = 8.

So plug in x for a, and 2 for b into the following:

(a^{3} - b^{3}) = (a^{2} +ab + b^{2})

Giving you:

(x^{3} - 8) = (x-2)(x^{2} + (x)(2) + 2^{2}) = (x-2)(x^{2} + 2x + 4)

Check

x(x^{2} +2x + 4) - 2(x^{2} + 2x + 4)

x^{3} **+2x**^{2} +4x **-2x**^{2}
-4x - 8

The x^{2} terms and the x terms cancel out and you are left with:

x^{3} - 8

Note that if it had been x^{3} + 8, the factors would be (x+2)(x^{2}-2x+4)

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

Randee S.

Dynamic, versatile tutor for core subject areas K-12

$8.75 per 15 min

View Profile >

Alexis G.

All-Subject/Test Prep Tutor, Specializing in Language Instruction

$11.25 per 15 min

View Profile >

Majdi J.

Patient and knowledgable Math tutor .

$10 per 15 min

View Profile >