document.write( "Question 610860: 11w(squared)-14w+3
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\n" ); document.write( "please show me how to work this promblem out!(: thanks \n" ); document.write( "

Algebra.Com's Answer #384627 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"11w%5E2-14w%2B3\"$ , we can see that the first coefficient is $\"11\"$ , the second coefficient is $\"-14\"$ , and the last term is $\"3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"11\"$ by the last term $\"3\"$ to get $\"%2811%29%283%29=33\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"33\"$ (the previous product) and add to the second coefficient $\"-14\"$ ?\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 $\"33\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"33\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-11,-33\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 $\"33\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*33 = 33
\n" ); document.write( "3*11 = 33
\n" ); document.write( "(-1)*(-33) = 33
\n" ); document.write( "(-3)*(-11) = 33\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 $\"-14\"$ :\r
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First Number	Second Number	Sum
1	33	1+33=34
3	11	3+11=14
-1	-33	-1+(-33)=-34
-3	-11	-3+(-11)=-14

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"-11\"$ add to $\"-14\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"-11\"$ both multiply to $\"33\"$ and add to $\"-14\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-14w\"$ with $\"-3w-11w\"$ . Remember, $\"-3\"$ and $\"-11\"$ add to $\"-14\"$ . So this shows us that $\"-3w-11w=-14w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"11w%5E2%2Bhighlight%28-3w-11w%29%2B3\"$ Replace the second term $\"-14w\"$ with $\"-3w-11w\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%2811w%5E2-3w%29%2B%28-11w%2B3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"w%2811w-3%29%2B%28-11w%2B3%29\"$ Factor out the GCF $\"w\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"w%2811w-3%29-1%2811w-3%29\"$ Factor out $\"1\"$ 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( " $\"%28w-1%29%2811w-3%29\"$ Combine like terms. Or factor out the common term $\"11w-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"11w%5E2-14w%2B3\"$ factors to $\"%28w-1%29%2811w-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"11w%5E2-14w%2B3=%28w-1%29%2811w-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28w-1%29%2811w-3%29\"$ to get $\"11w%5E2-14w%2B3\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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