document.write( "Question 384021: Factor.\r
\n" ); document.write( "\n" ); document.write( "3w^2 - 2w - 16 \n" ); document.write( "

Algebra.Com's Answer #271851 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3w%5E2-2w-16\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"-2\"$ , and the last term is $\"-16\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"-16\"$ to get $\"%283%29%28-16%29=-48\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-48\"$ (the previous product) and add to the second coefficient $\"-2\"$ ?\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 $\"-48\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-48\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,48\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-48\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 $\"-48\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-48) = -48
\n" ); document.write( "2*(-24) = -48
\n" ); document.write( "3*(-16) = -48
\n" ); document.write( "4*(-12) = -48
\n" ); document.write( "6*(-8) = -48
\n" ); document.write( "(-1)*(48) = -48
\n" ); document.write( "(-2)*(24) = -48
\n" ); document.write( "(-3)*(16) = -48
\n" ); document.write( "(-4)*(12) = -48
\n" ); document.write( "(-6)*(8) = -48\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 $\"-2\"$ :\r
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First Number	Second Number	Sum
1	-48	1+(-48)=-47
2	-24	2+(-24)=-22
3	-16	3+(-16)=-13
4	-12	4+(-12)=-8
6	-8	6+(-8)=-2
-1	48	-1+48=47
-2	24	-2+24=22
-3	16	-3+16=13
-4	12	-4+12=8
-6	8	-6+8=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"6\"$ and $\"-8\"$ add to $\"-2\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"6\"$ and $\"-8\"$ both multiply to $\"-48\"$ and add to $\"-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-2w\"$ with $\"6w-8w\"$ . Remember, $\"6\"$ and $\"-8\"$ add to $\"-2\"$ . So this shows us that $\"6w-8w=-2w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3w%5E2%2Bhighlight%286w-8w%29-16\"$ Replace the second term $\"-2w\"$ with $\"6w-8w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283w%5E2%2B6w%29%2B%28-8w-16%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"3w%28w%2B2%29%2B%28-8w-16%29\"$ Factor out the GCF $\"3w\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"3w%28w%2B2%29-8%28w%2B2%29\"$ Factor out $\"8\"$ 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( " $\"%283w-8%29%28w%2B2%29\"$ Combine like terms. Or factor out the common term $\"w%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"3w%5E2-2w-16\"$ factors to $\"%283w-8%29%28w%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"3w%5E2-2w-16=%283w-8%29%28w%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%283w-8%29%28w%2B2%29\"$ to get $\"3w%5E2-2w-16\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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