Algebra 1 Factoring Polynomials
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Fancy Factoring
Factoring Polynomials

 

 We look at "X times X + 4"

 like any other multiplication.
 

 
 Just do X times X then X times 4 
 and put the answers together.
 
 We could even multiply (X + 4) times (X + 4)
 Just multiply X + 4 times 4 
 and then multiply X + 4 times X.
 Then put the terms together in one place ...
 

 
 While it may be easy to see what's going on
 writing the multiplication like this,
 that's not the way it's usually written.
 It's usually written all on one line.
 
 We start like this ...

 (X + 4)(X + 4)

 
 Take the first term in the first brackets
 and multiply it by every term in the second bracket.
 

 
 Then take the second term in the first bracket
 and multiply it by every term in the second bracket.
 

 
 Now we combine terms where we can.
 An X 2 is not the same thing as an X.
 We can't combine them.
 We can combine the two different 4X terms we have.
 

(X + 4)(X + 4)   =   X2 + 4X + 4X + 16   =   X2 + 8X + 16

 
 The other way we did these problems was easier to follow,
 but this way uses a lot less paper to write.
 Math types love to save space,
 so this is the way it is usually done.
 
 More Examples:
 
 (X - 5)(3X + 2)   =   3X2 + 2X - 15X - 10   =   3X2 - 13X - 10
 
 (5X - 3)(X - 2)   =   5X2 - 10X - 3X + 6   =   5X2 - 13X + 6
 
 (-X + 5)(2X + 4)   =   -2X2 - 4X + 10X + 20   =   -2X2 + 6X + 20
 

   copyright 2005 Bruce Kirkpatrick

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