SOLUTION: Factor each polynomail completely what is the answer to the following 1. 45xcubed+15xsquared 2.zsquared-225

Question 615587: Factor each polynomail completely what is the answer to the following
1. 45xcubed+15xsquared
2.zsquared-225

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

When factoring, always start with the greatest common factor, GCF, if it is not a 1. The GCF here is :

Since the second factor above will not factor any further we are finished.

The GCF here is 1 and we almost never factor out a 1. So we proceed to other methods of factoring. I prefer to try the factoring patterns after the GCF.

Your expression has just two terms. There are three factoring patterns for two-term expressions. They are known as "sum of cubes", "difference of cubes" and "difference of squares". Since is not a perfect cube we cannot use either of the "cubes" patterns. is obviously a perfect square and we definitely have a difference. But is 225 a perfect square? Even if you do not immediately know whether 225 is a perfect square, you should be able, with just a little effort, to figure out that 225 is a perfect square! . So we do have a difference of squares and we can use that pattern, , to factor your expression:
(z+15)(z-15)
Ans since neither factor will factor further we are finished.
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