document.write( "Question 615587: Factor each polynomail completely what is the answer to the following
\n" ); document.write( "1. 45xcubed+15xsquared
\n" ); document.write( "2.zsquared-225
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #387271 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"45x%5E3-15x%5E2\"$
\n" ); document.write( "When factoring, always start with the greatest common factor, GCF, if it is not a 1. The GCF here is $\"15x%5E2\"$ :
\n" ); document.write( " $\"15x%5E2%283x-1%29\"$
\n" ); document.write( "Since the second factor above will not factor any further we are finished.

\n" ); document.write( " $\"z%5E2-225\"$
\n" ); document.write( "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.

\n" ); document.write( "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 $\"z%5E2\"$ is not a perfect cube we cannot use either of the \"cubes\" patterns. $\"z%5E2\"$ 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! $\"225+=+15%5E2\"$ . So we do have a difference of squares and we can use that pattern, $\"a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29\"$ , to factor your expression:
\n" ); document.write( "(z+15)(z-15)
\n" ); document.write( "Ans since neither factor will factor further we are finished. \n" ); document.write( "

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