SOLUTION: Hi, I'm learning about factoring out the greatest common factor and I am stuck. Could you please start this video at 6:05 minutes (https://www.youtube.com/watch?time_continue=360&v

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, I'm learning about factoring out the greatest common factor and I am stuck. Could you please start this video at 6:05 minutes (https://www.youtube.com/watch?time_continue=360&v      Log On


   

Question 1141802: Hi, I'm learning about factoring out the greatest common factor and I am stuck. Could you please start this video at 6:05 minutes (https://www.youtube.com/watch?time_continue=360&v=EDebmfT5Nsk) and help me with the problem #4?
He says that there are no common terms, and to use -1. My question is, why isn't Y considered a common term for this equation? Thanks in advance!!

Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
The expression for #4 is -y%5E3-2y%5E2%2By-7, and you want to factorize using greatest common factor.

Notice very obviously, -7 does NOT have a factor of y.
Here are the complete factorizations of the terms in the expression:
-1*y*y*y
-2*y*y
y
-1*7


There seems to be no common factor among those terms, but you can view y, if you want, as %28-1%29%28-1%29y, just so you may have -1 multiplied by an otherwise expression with a positive leading term of degree three. If you do this then you can give %28-1%29%28y%5E3%2B2y%5E2-y%2B7%29.

If you wanted to factorize with y, then you no longer have just a polynomial. You might have -1%2Ay%28y%5E2%2B2y-1%2B7%2Fy%29 but this is not so convenient a factorization because one of these factors is not polynomial.