can someone help me with this factoring
(x-3)^2 +5(x-3)

thank u
the answer is (x-3)(x+2)

Question

can someone help me with this factoring 
(x-3)^2 +5(x-3)

thank u
the answer is (x-3)(x+2)

anonymous · Answer

No matter how awkward or big a factor may be, if you see something in common between two terms, that thing can be factored out. So you have two terms, the (x-3)^2 and the 5(x-3). Well, each one of those has an (x-3) in it. So that means (x-3) can be removed from each group. First, let me rewrite:

(x-3)(x-3) + 5(x-3). Now I'll remove the common (x-3) from each group. When I pull that (x-3) out to the front, the first term leaves an (x-3) behind while the 2nd term leaves behind a 5.

|dw:1409369878377:dw|

You take the common term out in front, place parenthesis, then write what was not taken out inside of those parenthesis. As you can see, I have (x-3)[(x-3)+5]. What's inside of the parenthesis can easily be simplified to x-3+5 = x+2, leaving you with (x-3)(x+2). If that makes any sense.