Help with factoring

Question

Hi, 

 

I need some help with the steps involved in factoring this : 

 

(x—2)² + 3(x—2) 

Answer 1

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Answer 2

Alex,

 

(x - 2)² is the same thing as (x - 2)(x - 2)

 

So, we can rewrite the original like this:

 

(x - 2)(x - 2) + 3(x - 2)

 

Now, notice that both terms in the expression have (x - 2) as a factor.  So, factoring that out, we get:

 

(x - 2)(x - 2 + 3) = (x - 2)(x + 1)

 

Make sense?

Answer 3

(x - 2)² + 3(x - 2)

(x - 2)(x - 2) + 3(x - 2)           definition of squaring

(x - 2)((x - 2) + 3)                  factor out (x - 2)

(x - 2)(x + 1)                         combine like terms

Answer 4

First look for the greatest common factor, if there is any.  That common factor is (x - 2).

 

(x - 2)[(x - 2) + 3)]

 

 

Now we combine like terms where possible.

 

(x - 2)(x + 1)