document.write( "Question 414527: Hello! I was absent from my algebra lesson, and I have a queston on my homework.It asks that I solve the equasion. The equasion is -2h^2-28h-98 . I know so far that I need to put it in two different sets of parenthasees. So far, all I have written down is (-h ) (h ). Please help me, because I am very confused. Thank you! \n" ); document.write( "

Algebra.Com's Answer #290757 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"-2h%5E2-28h-98\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"-2%28h%5E2%2B14h%2B49%29\"$ Factor out the GCF $\"-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"h%5E2%2B14h%2B49\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"h%5E2%2B14h%2B49\"$ , we can see that the first coefficient is $\"1\"$ , the second coefficient is $\"14\"$ , and the last term is $\"49\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"1\"$ by the last term $\"49\"$ to get $\"%281%29%2849%29=49\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"49\"$ (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 $\"49\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"49\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-7,-49\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 $\"49\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*49 = 49
\n" ); document.write( "7*7 = 49
\n" ); document.write( "(-1)*(-49) = 49
\n" ); document.write( "(-7)*(-7) = 49\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	49	1+49=50
7	7	7+7=14
-1	-49	-1+(-49)=-50
-7	-7	-7+(-7)=-14

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"7\"$ and $\"7\"$ add to $\"14\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"7\"$ and $\"7\"$ both multiply to $\"49\"$ and add to $\"14\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"14h\"$ with $\"7h%2B7h\"$ . Remember, $\"7\"$ and $\"7\"$ add to $\"14\"$ . So this shows us that $\"7h%2B7h=14h\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"h%5E2%2Bhighlight%287h%2B7h%29%2B49\"$ Replace the second term $\"14h\"$ with $\"7h%2B7h\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%28h%5E2%2B7h%29%2B%287h%2B49%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28h%2B7%29%2B%287h%2B49%29\"$ Factor out the GCF $\"h\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28h%2B7%29%2B7%28h%2B7%29\"$ Factor out $\"7\"$ 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( " $\"%28h%2B7%29%28h%2B7%29\"$ Combine like terms. Or factor out the common term $\"h%2B7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"%28h%2B7%29%5E2\"$ Condense the terms.\r
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\n" ); document.write( "\n" ); document.write( "So $\"-2%28h%5E2%2B14h%2B49%29\"$ then factors further to $\"-2%28h%2B7%29%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"-2h%5E2-28h-98\"$ completely factors to $\"-2%28h%2B7%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"-2h%5E2-28h-98=-2%28h%2B7%29%5E2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"-2%28h%2B7%29%5E2\"$ to get $\"-2h%5E2-28h-98\"$ 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, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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