document.write( "Question 76766: Factor - x2 - 10x - 56 \n" ); document.write( "
Algebra.Com's Answer #55031 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
First factor out a negative 1\r
\n" ); document.write( "\n" ); document.write( "\"-1%28x%5E2%2B10x%2B56%29\"\r
\n" ); document.write( "\n" ); document.write( "Now factor the quadratic in the parenthesis:\r
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Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B10%2Ax%2B56\", first we need to ask ourselves: What two numbers multiply to 56 and add to 10? Lets find out by listing all of the possible factors of 56
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1,2,4,7,8,14,28,56,
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\n" ); document.write( " -1,-2,-4,-7,-8,-14,-28,-56,List the negative factors as well. This will allow us to find all possible combinations
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\n" ); document.write( " These factors pair up to multiply to 56.
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\n" ); document.write( " 1*56=56
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\n" ); document.write( " 2*28=56
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\n" ); document.write( " 4*14=56
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\n" ); document.write( " 7*8=56
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\n" ); document.write( " (-1)*(-56)=56
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\n" ); document.write( " (-2)*(-28)=56
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\n" ); document.write( " (-4)*(-14)=56
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\n" ); document.write( " (-7)*(-8)=56
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\n" ); document.write( " note: remember two negative numbers multiplied together make a positive number
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\n" ); document.write( " Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10
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First Number|Second Number|Sum
1|56|1+56=57
2|28|2+28=30
4|14|4+14=18
7|8|7+8=15
-1|-56|-1+(-56)=-57
-2|-28|-2+(-28)=-30
-4|-14|-4+(-14)=-18
-7|-8|-7+(-8)=-15
\r\n" ); document.write( " \r\n" ); document.write( " None of these factors add to 10. So this quadratic cannot be factored. In order to solve for x, we need to use the quadratic formula.\n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "So the quadratic \"-x%5E2-10x-56\" cannot be factored \n" ); document.write( "
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