How to Simplify Factorization?

[alpha01]

Factorize:
x^3 − 2x^2 − 4x + 8 correct answer:

(x^3 − 2x^2) − (4x − 8)

x^2(x − 2) − 4(x − 2)

(x^2 − 4)(x − 2)

(x − 2)(x + 2)(x − 2)

(x − 2) 2(x + 2)

In the third line where the terms are grouped i don't understand why one of the (x - 2) is omitted? i.e shouldn't it be (x -2)^2 ?

 

[alpha01]

Sorry just realized this should be under the "homework" section. Will post homework questions there in future (in the meantime could a mod please move it there)..

 

[alpha01]

can anyone help please? Its too critical and basic to go any further in the course notes until i understand this

 

[Ephratah7]

... What is ^?

 

[CRGreathouse]

can anyone help please? Its too critical and basic to go any further in the course notes until i understand this

(x^2 - 4) = (x - 2)(x + 2), so one of the (x - 2) factors was "hiding inside" the (x^2 - 4).

 

[qspeechc]

Going from:x^2(x − 2) − 4(x − 2)
to:(x^2 − 4)(x − 2)
is your problem? Well consider this:
ab - cb = b(a - c)
Do you agree? If we multiply out on the right we get the left-hand side. Now in your example, a = x^2, b=(x-2), c=4.
Do you see how it works now?

 

[alpha01]

Going from:x^2(x − 2) − 4(x − 2)
to:(x^2 − 4)(x − 2)
is your problem? Well consider this:
ab - cb = b(a - c)
Do you agree? If we multiply out on the right we get the left-hand side. Now in your example, a = x^2, b=(x-2), c=4.
Do you see how it works now?

thank you