document.write( "Question 245969: I was wondering if you could show me how to factor this equation: 7a2+53a+28
\n" ); document.write( "This is the work I got to but then I could go no father.\r
\n" ); document.write( "\n" ); document.write( "I used the x-box to find the answer.\r
\n" ); document.write( "\n" ); document.write( "After the x-box I got\r
\n" ); document.write( "\n" ); document.write( "(a+7)(7a+7)
\n" ); document.write( "7a2+56a+28 which does not equal the original question.
\n" ); document.write( "(when it says 7a2 it means 7 times a squared) \n" ); document.write( "

Algebra.Com's Answer #179649 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"7a%5E2%2B53a%2B28\"$ , we can see that the first coefficient is $\"7\"$ , the second coefficient is $\"53\"$ , and the last term is $\"28\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"7\"$ by the last term $\"28\"$ to get $\"%287%29%2828%29=196\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"196\"$ (the previous product) and add to the second coefficient $\"53\"$ ?\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 $\"196\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"196\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,7,14,28,49,98,196\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-7,-14,-28,-49,-98,-196\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 $\"196\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*196 = 196
\n" ); document.write( "2*98 = 196
\n" ); document.write( "4*49 = 196
\n" ); document.write( "7*28 = 196
\n" ); document.write( "14*14 = 196
\n" ); document.write( "(-1)*(-196) = 196
\n" ); document.write( "(-2)*(-98) = 196
\n" ); document.write( "(-4)*(-49) = 196
\n" ); document.write( "(-7)*(-28) = 196
\n" ); document.write( "(-14)*(-14) = 196\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 $\"53\"$ :\r
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First Number	Second Number	Sum
1	196	1+196=197
2	98	2+98=100
4	49	4+49=53
7	28	7+28=35
14	14	14+14=28
-1	-196	-1+(-196)=-197
-2	-98	-2+(-98)=-100
-4	-49	-4+(-49)=-53
-7	-28	-7+(-28)=-35
-14	-14	-14+(-14)=-28

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"4\"$ and $\"49\"$ add to $\"53\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"4\"$ and $\"49\"$ both multiply to $\"196\"$ and add to $\"53\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"53a\"$ with $\"4a%2B49a\"$ . Remember, $\"4\"$ and $\"49\"$ add to $\"53\"$ . So this shows us that $\"4a%2B49a=53a\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"7a%5E2%2Bhighlight%284a%2B49a%29%2B28\"$ Replace the second term $\"53a\"$ with $\"4a%2B49a\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%287a%5E2%2B4a%29%2B%2849a%2B28%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"a%287a%2B4%29%2B%2849a%2B28%29\"$ Factor out the GCF $\"a\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"a%287a%2B4%29%2B7%287a%2B4%29\"$ 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( " $\"%28a%2B7%29%287a%2B4%29\"$ Combine like terms. Or factor out the common term $\"7a%2B4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"7a%5E2%2B53a%2B28\"$ factors to $\"%28a%2B7%29%287a%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"7a%5E2%2B53a%2B28=%28a%2B7%29%287a%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28a%2B7%29%287a%2B4%29\"$ to get $\"7a%5E2%2B53a%2B28\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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