document.write( "Question 376723: The number of hot dogs sold at the concession stand during each hour h after opening at a s0ccer tournament is given by the polynomial 2h^2-19h+24. write this polonomial in factored form.
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Algebra.Com's Answer #267977 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2h%5E2-19h%2B24\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"-19\"$ , and the last term is $\"24\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"24\"$ to get $\"%282%29%2824%29=48\"$ .\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 $\"-19\"$ ?\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 $\"-19\"$ :\r
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First Number	Second Number	Sum
1	48	1+48=49
2	24	2+24=26
3	16	3+16=19
4	12	4+12=16
6	8	6+8=14
-1	-48	-1+(-48)=-49
-2	-24	-2+(-24)=-26
-3	-16	-3+(-16)=-19
-4	-12	-4+(-12)=-16
-6	-8	-6+(-8)=-14

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"-16\"$ add to $\"-19\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"-16\"$ both multiply to $\"48\"$ and add to $\"-19\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-19h\"$ with $\"-3h-16h\"$ . Remember, $\"-3\"$ and $\"-16\"$ add to $\"-19\"$ . So this shows us that $\"-3h-16h=-19h\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2h%5E2%2Bhighlight%28-3h-16h%29%2B24\"$ Replace the second term $\"-19h\"$ with $\"-3h-16h\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%282h%5E2-3h%29%2B%28-16h%2B24%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"h%282h-3%29%2B%28-16h%2B24%29\"$ Factor out the GCF $\"h\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"h%282h-3%29-8%282h-3%29\"$ 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( " $\"%28h-8%29%282h-3%29\"$ Combine like terms. Or factor out the common term $\"2h-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"2h%5E2-19h%2B24\"$ factors to $\"%28h-8%29%282h-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2h%5E2-19h%2B24=%28h-8%29%282h-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28h-8%29%282h-3%29\"$ to get $\"2h%5E2-19h%2B24\"$ 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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