Algebra 1 Introduction to Factoring
Math-Prof HOME Algebra 1 Table of Contents Ask A Question PREV NEXT

The X Factor
Introduction to Factoring

 

 So what do we do with something like:

 

X2 + 4X = 0

 
 X 2 and X are not the same thing.
 We can't just combine them together.
 BUT, what we can do is something called factoring.
 
 What's that?
 
 Well you know that X times X equals X 2.
 and also X times 4 equals 4X so:
 

 X times (X + 4) equals X2 + 4X

 
 STOP! TIME OUT! WHOA! HOLD ON!
 
 Let's go through that one more time in slow motion ...
 
 OK, OK.
 
 If we multiply 6 times 12,
 what do we actually do?
 

 
 First we multiply the 6 times the 2 
 and write that down.
 
 Then we multiply the 6 times the 10
 and write that down.
 
 The 12 is like a 10 plus a 2.
 

 
 Then we add the 12 and the 60
 and get 72 ...
 

 
 OK, that one we know.
 Now we have X + 4 times X
 

 
 We multiply X times X and write that down.
 Then we multiply the X times 4 and write that down.
 Then we add those two together ...
 

 
 It's a little tougher to start with X 2 + 4X
 and figure out what we multiplied together to get it.
 
 But hey, we're big shot algebra types now,
 we can handle it!
 
 That means we can rewrite:

 

  X2 + 4X = 0   as   X(X + 4) = 0

 
 Great, just what does THAT get us?
 
 Well, it's like this,
 if you multiply two things together and get zero
 then one or the other of the things 
 MUST be equal to zero.
 
 So in X(X + 4) = 0 we know that either
 X = 0 or X + 4 = 0
 
 For the X = 0 part, there's nothing to do.
 X = 0 and that's that.
 
 But we need to do a little work 
 to find X when we have X + 4 = 0.
 It's an easy one ...
 

 
 So our two answers are X = 0 and X = -4. 
 Either one of those numbers could be put in place of X
 in the equation ...
 

X2 + 4X = 0

 
 and the thing would be true.
 
 Let's check and see ...
 

 Since the terms we get at the end
 on each side of the = ARE equal to each other
 the answers we are testing do work.
 

   copyright 2005 Bruce Kirkpatrick

Math-Prof HOME Algebra 1 Table of Contents Ask A Question PREV NEXT