document.write( "Question 143273: x^2 – 16x + 63
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Algebra.Com's Answer #104260 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to factor?\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"x%5E2-16x%2B63\"$ we can see that the first term is $\"x%5E2\"$ and the last term is $\"63\"$ where the coefficients are 1 and 63 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 63 to get 63. Now what two numbers multiply to 63 and add to the middle coefficient -16? Let's list all of the factors of 63:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 63:\r
\n" ); document.write( "\n" ); document.write( "1,3,7,9,21,63\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-7,-9,-21,-63 ...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 63\r
\n" ); document.write( "\n" ); document.write( "1*63\r
\n" ); document.write( "\n" ); document.write( "3*21\r
\n" ); document.write( "\n" ); document.write( "7*9\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-63)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-21)\r
\n" ); document.write( "\n" ); document.write( "(-7)*(-9)\r
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\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -16\r
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First Number	Second Number	Sum
1	63	1+63=64
3	21	3+21=24
7	9	7+9=16
-1	-63	-1+(-63)=-64
-3	-21	-3+(-21)=-24
-7	-9	-7+(-9)=-16

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -7 and -9 add up to -16 and multiply to 63\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"x%5E2-16x%2B63\"$ , replace $\"-16x\"$ with $\"-7x%2B-9x\"$ (notice $\"-7x%2B-9x\"$ adds up to $\"-16x\"$ . So it is equivalent to $\"-16x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28-7x%2B-9x%29%2B63\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"x%5E2-7x-9x%2B63\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-7x%29%2B%28-9x%2B63%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-7%29-9%28x-7%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-9\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-9%29%28x-7%29\"$ Since we have a common term of $\"x-7\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-7x-9x%2B63\"$ factors to $\"%28x-9%29%28x-7%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"x%5E2-16x%2B63\"$ factors to $\"%28x-9%29%28x-7%29\"$ (since $\"x%5E2-16x%2B63\"$ is equivalent to $\"x%5E2-7x-9x%2B63\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-16x%2B63\"$ factors to $\"%28x-9%29%28x-7%29\"$
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