document.write( "Question 374474: I have a hard time factoring. Please help!
\n" ); document.write( "Factor completely.
\n" ); document.write( "7x^6-63x^5+14x^4 \n" ); document.write( "

Algebra.Com's Answer #266412 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"7x%5E6-63x%5E5%2B14x%5E4\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%5E4%28x%5E2-9x%2B2%29\"$ Factor out the GCF $\"7x%5E4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"x%5E2-9x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"x%5E2-9x%2B2\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"-9\"$ , and the last term is $\"2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"2\"$ to get $\"%281%29%282%29=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"2\"$ (the previous product) and add to the second coefficient $\"-9\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"2\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"2\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. This will allow us to find all possible combinations.\r
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\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to $\"2\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*2 = 2
\n" ); document.write( "(-1)*(-2) = 2\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"-9\"$ :\r
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First Number	Second Number	Sum
1	2	1+2=3
-1	-2	-1+(-2)=-3

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that there are no pairs of numbers which add to $\"-9\"$ . So $\"x%5E2-9x%2B2\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"7x%5E6-63x%5E5%2B14x%5E4\"$ simply factors to $\"7x%5E4%28x%5E2-9x%2B2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"7x%5E6-63x%5E5%2B14x%5E4=7x%5E4%28x%5E2-9x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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