document.write( "Question 182956: C6x²+7x-20 \n" ); document.write( "

Algebra.Com's Answer #137353 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"6x%5E2%2B7x-20\"$ , we can see that the first coefficient is $\"6\"$ , the second coefficient is $\"7\"$ , and the last term is $\"-20\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"6\"$ by the last term $\"-20\"$ to get $\"%286%29%28-20%29=-120\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-120\"$ (the previous product) and add to the second coefficient $\"7\"$ ?\r
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\n" ); document.write( "\n" ); document.write( "To find these two numbers, we need to list all of the factors of $\"-120\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-120\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120\r
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\n" ); document.write( "\n" ); document.write( "Note: list the negative of each factor. 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 $\"-120\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-120)
\n" ); document.write( "2*(-60)
\n" ); document.write( "3*(-40)
\n" ); document.write( "4*(-30)
\n" ); document.write( "5*(-24)
\n" ); document.write( "6*(-20)
\n" ); document.write( "8*(-15)
\n" ); document.write( "10*(-12)
\n" ); document.write( "(-1)*(120)
\n" ); document.write( "(-2)*(60)
\n" ); document.write( "(-3)*(40)
\n" ); document.write( "(-4)*(30)
\n" ); document.write( "(-5)*(24)
\n" ); document.write( "(-6)*(20)
\n" ); document.write( "(-8)*(15)
\n" ); document.write( "(-10)*(12)\r
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\n" ); document.write( "\n" ); document.write( "Now let's add up each pair of factors to see if one pair adds to the middle coefficient $\"7\"$ :\r
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First Number	Second Number	Sum
1	-120	1+(-120)=-119
2	-60	2+(-60)=-58
3	-40	3+(-40)=-37
4	-30	4+(-30)=-26
5	-24	5+(-24)=-19
6	-20	6+(-20)=-14
8	-15	8+(-15)=-7
10	-12	10+(-12)=-2
-1	120	-1+120=119
-2	60	-2+60=58
-3	40	-3+40=37
-4	30	-4+30=26
-5	24	-5+24=19
-6	20	-6+20=14
-8	15	-8+15=7
-10	12	-10+12=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-8\"$ and $\"15\"$ add to $\"7\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-8\"$ and $\"15\"$ both multiply to $\"-120\"$ and add to $\"7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"7x\"$ with $\"-8x%2B15x\"$ . Remember, $\"-8\"$ and $\"15\"$ add to $\"7\"$ . So this shows us that $\"-8x%2B15x=7x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"6x%5E2%2Bhighlight%28-8x%2B15x%29-20\"$ Replace the second term $\"7x\"$ with $\"-8x%2B15x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%286x%5E2-8x%29%2B%2815x-20%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%283x-4%29%2B%2815x-20%29\"$ Factor out the GCF $\"2x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%283x-4%29%2B5%283x-4%29\"$ Factor out $\"5\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%2B5%29%283x-4%29\"$ Combine like terms. Or factor out the common term $\"3x-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"6x%5E2%2B7x-20\"$ factors to $\"%282x%2B5%29%283x-4%29\"$ .\r
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