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How do I factor by grouping?

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1 Answer

Factoring is a big topic - too big to address adequately in this short space.  Try looking over this lesson on factoring. 
 
 
If you have specific questions, or would like a specific equation factored, post it here and we'll help.
 
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126x3-54x2-210x+90
 
Group as follows:
 
(126x3-54x2) - (210x-90)
 
You can factor an 18x2 out of the terms in the first parentheses and a 30 out of the terms in the second parentheses:
 
18x2(7x-3) - 30(7x-3)
 
Now factor out the (7x-3):
 
(18x2-30)(7x-3)
 
Finally, I can factor out a 6 from the terms in the first parentheses:
 
6(3x2-5)(7x-3)
 
Check by multiplying out the factored expression (FOIL) to verify that you get the original expression back.

Comments

Could you give me simple
step by step instructions on how to fctor this expression:
126x^3-54x^2-210x+90
If you can I would very much appreciate it.
BTW: 126x^3.   = 126x cubed
126x3-54x2-210x+90
 
Let's group the first 2 terms together and the last two together:
 
(126x3-54x2) - (210x-90)
 
I can factor out 18x2 out of (126x3-54x2)
 
(126x3-54x2) = 18x2(7x-3)
 
I can factor a 30 out of the second two terms:
 
(210x-90) = 30(7x-3)
 
Combining:
 
(126x3-54x2) - (210x-90) = 18x2(7x-3) - 30(7x-3)
 
Finally, factor the (7x-3) out of the two terms:
 
18x2(7x-3) - 30(7x-3) = (18x2-30)(7x-3)
 
Finally, I can factor a 6 out of the (18x2-30) term:
 
6(3x2-5)(7x-3)
 
Check by FOILing it to see if you get the original expression.