FACTORING



Sometimes we cannot factor because there are no common factors. 

For example 4t + 9 = 2(2)t + 3(3)

Multiply (r + 3)(r + 3)   = answer

Now reverse the procedure and factor r2 + 6r + 9  = (        )(        )

The first terms in the parenthesis when multiplied together must equal r2 and the second terms when multiplied together must equal + 9.  How do we obtain the middle term? Notice that when we add 3 + 3 together we get 6.

How do I know that p2 + 8p + 16 will equal (p + 4)(p + 4)?  I used a very important and old mathematical principal.

I guessed!

After you do enough of these problems it becomes an educated guess.   To verify that the answer is correct multiply (p + 4)(p + 4) and see if the results equals p2 + 8p + 16.  If it does, the answer is correct.

Factor these examples:

      
  1.    r2 - r - 20 =  answer
  2.    6t2 - 8t - 8 =  answer
  3.    24p2 - 34p + 12 =  answer

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