document.write( "Question 368621: Hello. Can you please help me? It's greatly appreciated.\r
\n" ); document.write( "\n" ); document.write( "solve equation by factoring:\r
\n" ); document.write( "\n" ); document.write( "3x^2 - 13x -10 thank you! \n" ); document.write( "

Algebra.Com's Answer #262658 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'll show you how to factor it.\r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"3x%5E2-13x-10\"$ we can see that the first term is $\"3x%5E2\"$ and the last term is $\"-10\"$ where the coefficients are 3 and -10 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 3 and the last coefficient -10 to get -30. Now what two numbers multiply to -30 and add to the middle coefficient -13? Let's list all of the factors of -30:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -30:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,5,6,10,15,30\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-5,-6,-10,-15,-30 ...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 -30\r
\n" ); document.write( "\n" ); document.write( "(1)*(-30)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-15)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(30)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(15)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(10)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(6)\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 -13? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -13\r
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First Number	Second Number	Sum
1	-30	1+(-30)=-29
2	-15	2+(-15)=-13
3	-10	3+(-10)=-7
5	-6	5+(-6)=-1
-1	30	-1+30=29
-2	15	-2+15=13
-3	10	-3+10=7
-5	6	-5+6=1

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 2 and -15 add up to -13 and multiply to -30\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"3x%5E2-13x-10\"$ , replace $\"-13x\"$ with $\"2x%2B-15x\"$ (notice $\"2x%2B-15x\"$ adds up to $\"-13x\"$ . So it is equivalent to $\"-13x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2%2Bhighlight%282x%2B-15x%29%2B-10\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"3x%5E2%2B2x-15x-10\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x%5E2%2B2x%29%2B%28-15x-10%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x%2B2%29-5%283x%2B2%29\"$ 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( " $\"%28x-5%29%283x%2B2%29\"$ Since we have a common term of $\"3x%2B2\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B2x-15x-10\"$ factors to $\"%28x-5%29%283x%2B2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"3x%5E2-13x-10\"$ factors to $\"%28x-5%29%283x%2B2%29\"$ (since $\"3x%5E2-13x-10\"$ is equivalent to $\"3x%5E2%2B2x-15x-10\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2-13x-10\"$ factors to $\"%28x-5%29%283x%2B2%29\"$
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