document.write( "Question 133006: Factor the trinomial.\r
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Algebra.Com's Answer #97213 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"v%5E3-4v%5E2-21v\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"v%28v%5E2-4v-21%29\"$ Factor out the GCF $\"v\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"v%5E2-4v-21\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"1v%5E2-4v-21\"$ we can see that the first term is $\"1v%5E2\"$ and the last term is $\"-21\"$ where the coefficients are 1 and -21 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -21 to get -21. Now what two numbers multiply to -21 and add to the middle coefficient -4? Let's list all of the factors of -21:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -21:\r
\n" ); document.write( "\n" ); document.write( "1,3,7,21\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-7,-21 ...List the negative factors as well. 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 -21\r
\n" ); document.write( "\n" ); document.write( "(1)*(-21)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-7)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(21)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(7)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4\r
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First Number	Second Number	Sum
1	-21	1+(-21)=-20
3	-7	3+(-7)=-4
-1	21	-1+21=20
-3	7	-3+7=4

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 3 and -7 add up to -4 and multiply to -21\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1v%5E2-4v-21\"$ , replace $\"-4v\"$ with $\"3v%2B-7v\"$ (notice $\"3v%2B-7v\"$ adds up to $\"-4v\"$ . So it is equivalent to $\"-4v\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1v%5E2%2Bhighlight%283v%2B-7v%29%2B-21\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1v%5E2%2B3v-7v-21\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281v%5E2%2B3v%29%2B%28-7v-21%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"v%28v%2B3%29-7%28v%2B3%29\"$ Factor out the GCF of $\"v\"$ out of the first group. Factor out the GCF of $\"-7\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28v-7%29%28v%2B3%29\"$ Since we have a common term of $\"v%2B3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1v%5E2%2B3v-7v-21\"$ factors to $\"%28v-7%29%28v%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1v%5E2-4v-21\"$ factors to $\"%28v-7%29%28v%2B3%29\"$ (since $\"1v%5E2-4v-21\"$ is equivalent to $\"1v%5E2%2B3v-7v-21\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"v%28v%5E2-4v-21%29\"$ and factors further to $\"v%28v-7%29%28v%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"v%5E3-4v%5E2-21v\"$ factors to $\"v%28v-7%29%28v%2B3%29\"$ \r
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