document.write( "Question 221654: I have another problem that i do not understand. Help please! 5w2-18w+9 of course the 2 after the w is supposed to be a little tiny 2 a bit above the w. Thank you for your help. \n" ); document.write( "

Algebra.Com's Answer #166197 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"5w%5E2-18w%2B9\"$ , we can see that the first coefficient is $\"5\"$ , the second coefficient is $\"-18\"$ , and the last term is $\"9\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"5\"$ by the last term $\"9\"$ to get $\"%285%29%289%29=45\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"45\"$ (the previous product) and add to the second coefficient $\"-18\"$ ?\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 $\"45\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"45\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,3,5,9,15,45\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 $\"45\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*45 = 45
\n" ); document.write( "3*15 = 45
\n" ); document.write( "5*9 = 45
\n" ); document.write( "(-1)*(-45) = 45
\n" ); document.write( "(-3)*(-15) = 45
\n" ); document.write( "(-5)*(-9) = 45\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 $\"-18\"$ :\r
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First Number	Second Number	Sum
1	45	1+45=46
3	15	3+15=18
5	9	5+9=14
-1	-45	-1+(-45)=-46
-3	-15	-3+(-15)=-18
-5	-9	-5+(-9)=-14

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"-15\"$ add to $\"-18\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"-15\"$ both multiply to $\"45\"$ and add to $\"-18\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-18w\"$ with $\"-3w-15w\"$ . Remember, $\"-3\"$ and $\"-15\"$ add to $\"-18\"$ . So this shows us that $\"-3w-15w=-18w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5w%5E2%2Bhighlight%28-3w-15w%29%2B9\"$ Replace the second term $\"-18w\"$ with $\"-3w-15w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%285w%5E2-3w%29%2B%28-15w%2B9%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"w%285w-3%29%2B%28-15w%2B9%29\"$ Factor out the GCF $\"w\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"w%285w-3%29-3%285w-3%29\"$ Factor out $\"3\"$ 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( " $\"%28w-3%29%285w-3%29\"$ Combine like terms. Or factor out the common term $\"5w-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"5w%5E2-18w%2B9\"$ factors to $\"%28w-3%29%285w-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"5w%5E2-18w%2B9=%28w-3%29%285w-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28w-3%29%285w-3%29\"$ to get $\"5w%5E2-18w%2B9\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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