document.write( "Question 207959: How can I do the factoring of the following: N to the forth power minus 4N to the 3rd power plus n minus 4 \n" ); document.write( "

Algebra.Com's Answer #157290 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"n%5E4-4n%5E3%2Bn-4\"$ Start with the given expression\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28n%5E4-4n%5E3%29%2B%28n-4%29\"$ Group like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"n%5E3%28n-4%29%2B1%28n-4%29\"$ Factor out the GCF $\"n%5E3\"$ out of the first group. Factor out the GCF $\"1\"$ out of the second group\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28n%5E3%2B1%29%28n-4%29\"$ Since we have the common term $\"n-4\"$ , we can combine like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28n%2B1%29%28n%5E2-n%2B1%29%28n-4%29\"$ Now factor $\"n%5E3%2B1\"$ to get $\"%28n%2B1%29%28n%5E2-n%2B1%29\"$ (hint: use the sum of cubes formula)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28n%2B1%29%28n-4%29%28n%5E2-n%2B1%29\"$ Rearrange the terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"n%5E4-4n%5E3%2Bn-4\"$ completely factors to $\"%28n%2B1%29%28n-4%29%28n%5E2-n%2B1%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In other words, $\"n%5E4-4n%5E3%2Bn-4=%28n%2B1%29%28n-4%29%28n%5E2-n%2B1%29\"$ \n" ); document.write( "

\n" );