document.write( "Question 145795: I have two questions if that's okay...\r
\n" ); document.write( "\n" ); document.write( "1. Can you show me, step by step, how to find the factors of x^2 – 5x – 6\r
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Algebra.Com's Answer #106403 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"x%5E2-5x-6\"$ we can see that the first term is $\"x%5E2\"$ and the last term is $\"-6\"$ where the coefficients are 1 and -6 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient -5? Let's list all of the factors of -6:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -6:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6 ...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 -6\r
\n" ); document.write( "\n" ); document.write( "(1)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-3)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(6)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(3)\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 -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5\r
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First Number	Second Number	Sum
1	-6	1+(-6)=-5
2	-3	2+(-3)=-1
-1	6	-1+6=5
-2	3	-2+3=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 1 and -6 add up to -5 and multiply to -6\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"x%5E2-5x-6\"$ , replace $\"-5x\"$ with $\"x%2B-6x\"$ (notice $\"x%2B-6x\"$ adds up to $\"-5x\"$ . So it is equivalent to $\"-5x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%28x%2B-6x%29%2B-6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"x%5E2%2Bx-6x-6\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2Bx%29%2B%28-6x-6%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B1%29-6%28x%2B1%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-6\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-6%29%28x%2B1%29\"$ Since we have a common term of $\"x%2B1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2Bx-6x-6\"$ factors to $\"%28x-6%29%28x%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"x%5E2-5x-6\"$ factors to $\"%28x-6%29%28x%2B1%29\"$ (since $\"x%5E2-5x-6\"$ is equivalent to $\"x%5E2%2Bx-6x-6\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-5x-6\"$ factors to $\"%28x-6%29%28x%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"x%5E2-x-20\"$ we can see that the first term is $\"x%5E2\"$ and the last term is $\"-20\"$ where the coefficients are 1 and -20 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -20 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient -1? Let's list all of the factors of -20:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -20:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20 ...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 -20\r
\n" ); document.write( "\n" ); document.write( "(1)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-5)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(20)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(10)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(5)\r
\n" ); document.write( "
\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 -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1\r
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First Number	Second Number	Sum
1	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 4 and -5 add up to -1 and multiply to -20\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"x%5E2-x-20\"$ , replace $\"-x\"$ with $\"4x%2B-5x\"$ (notice $\"4x%2B-5x\"$ adds up to $\"-x\"$ . So it is equivalent to $\"-x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2Bhighlight%284x%2B-5x%29%2B-20\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"x%5E2%2B4x-5x-20\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B4x%29%2B%28-5x-20%29\"$ Group like terms\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B4%29-5%28x%2B4%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-5\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-5%29%28x%2B4%29\"$ Since we have a common term of $\"x%2B4\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2%2B4x-5x-20\"$ factors to $\"%28x-5%29%28x%2B4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"x%5E2-x-20\"$ factors to $\"%28x-5%29%28x%2B4%29\"$ (since $\"x%5E2-x-20\"$ is equivalent to $\"x%5E2%2B4x-5x-20\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E2-x-20\"$ factors to $\"%28x-5%29%28x%2B4%29\"$
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