document.write( "Question 188535: 24x^2-37-5
\n" ); document.write( "my teacher taugt us lIke multi:AC then subtract to get -37
\n" ); document.write( "0k so 24*5=120 then she said see what all goes into that number
\n" ); document.write( "then when u found it see if it is the same is B which is -37..
\n" ); document.write( "i got -40+3 is -37
\n" ); document.write( "but when i put it all together
\n" ); document.write( "24x^2-40x+3x-5
\n" ); document.write( "4x(6x-10)+1(3x-5) and Its suppose to be the same
\n" ); document.write( "i get lost can u help me im hopin u can understand wat im sayin
\n" ); document.write( "thats the best way i can explain it \n" ); document.write( "

Algebra.Com's Answer #141366 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"24x%5E2-37x-5\"$ , we can see that the first coefficient is $\"24\"$ , the second coefficient is $\"-37\"$ , and the last term is $\"-5\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"24\"$ by the last term $\"-5\"$ to get $\"%2824%29%28-5%29=-120\"$ .\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 $\"-37\"$ ?\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 $\"-37\"$ :\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 $\"3\"$ and $\"-40\"$ add to $\"-37\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"3\"$ and $\"-40\"$ both multiply to $\"-120\"$ and add to $\"-37\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-37x\"$ with $\"3x-40x\"$ . Remember, $\"3\"$ and $\"-40\"$ add to $\"-37\"$ . So this shows us that $\"3x-40x=-37x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"24x%5E2%2Bhighlight%283x-40x%29-5\"$ Replace the second term $\"-37x\"$ with $\"3x-40x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%2824x%5E2%2B3x%29%2B%28-40x-5%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%288x%2B1%29%2B%28-40x-5%29\"$ Factor out the GCF $\"3x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%288x%2B1%29-5%288x%2B1%29\"$ 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( " $\"%283x-5%29%288x%2B1%29\"$ Combine like terms. Or factor out the common term $\"8x%2B1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"24x%5E2-37x-5\"$ factors to $\"%283x-5%29%288x%2B1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by FOILing $\"%283x-5%29%288x%2B1%29\"$ to get $\"24x%5E2-37x-5\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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