document.write( "Question 704617: Can you please help me factor this equation?
\n" ); document.write( "16x^2-86x+30
\n" ); document.write( "I removed 2 so I have 2(8x^2-43x+15)
\n" ); document.write( "I don't know where to go from here...thank you! \n" ); document.write( "

Algebra.Com's Answer #434181 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"16x%5E2-86x%2B30\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"2%288x%5E2-43x%2B15%29\"$ 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 $\"8x%5E2-43x%2B15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"8x%5E2-43x%2B15\"$ , we can see that the first coefficient is $\"8\"$ , the second coefficient is $\"-43\"$ , and the last term is $\"15\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"8\"$ by the last term $\"15\"$ to get $\"%288%29%2815%29=120\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"120\"$ (the previous product) and add to the second coefficient $\"-43\"$ ?\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 $\"120\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"120\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-8,-10,-12,-15,-20,-24,-30,-40,-60,-120\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 $\"120\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*120 = 120
\n" ); document.write( "2*60 = 120
\n" ); document.write( "3*40 = 120
\n" ); document.write( "4*30 = 120
\n" ); document.write( "5*24 = 120
\n" ); document.write( "6*20 = 120
\n" ); document.write( "8*15 = 120
\n" ); document.write( "10*12 = 120
\n" ); document.write( "(-1)*(-120) = 120
\n" ); document.write( "(-2)*(-60) = 120
\n" ); document.write( "(-3)*(-40) = 120
\n" ); document.write( "(-4)*(-30) = 120
\n" ); document.write( "(-5)*(-24) = 120
\n" ); document.write( "(-6)*(-20) = 120
\n" ); document.write( "(-8)*(-15) = 120
\n" ); document.write( "(-10)*(-12) = 120\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 $\"-43\"$ :\r
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First Number	Second Number	Sum
1	120	1+120=121
2	60	2+60=62
3	40	3+40=43
4	30	4+30=34
5	24	5+24=29
6	20	6+20=26
8	15	8+15=23
10	12	10+12=22
-1	-120	-1+(-120)=-121
-2	-60	-2+(-60)=-62
-3	-40	-3+(-40)=-43
-4	-30	-4+(-30)=-34
-5	-24	-5+(-24)=-29
-6	-20	-6+(-20)=-26
-8	-15	-8+(-15)=-23
-10	-12	-10+(-12)=-22

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"-40\"$ add to $\"-43\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"-40\"$ both multiply to $\"120\"$ and add to $\"-43\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-43x\"$ with $\"-3x-40x\"$ . Remember, $\"-3\"$ and $\"-40\"$ add to $\"-43\"$ . So this shows us that $\"-3x-40x=-43x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"8x%5E2%2Bhighlight%28-3x-40x%29%2B15\"$ Replace the second term $\"-43x\"$ with $\"-3x-40x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%288x%5E2-3x%29%2B%28-40x%2B15%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%288x-3%29%2B%28-40x%2B15%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%288x-3%29-5%288x-3%29\"$ Factor out $\"5\"$ 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( " $\"%28x-5%29%288x-3%29\"$ Combine like terms. Or factor out the common term $\"8x-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"2%288x%5E2-43x%2B15%29\"$ then factors further to $\"2%28x-5%29%288x-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"16x%5E2-86x%2B30\"$ completely factors to $\"2%28x-5%29%288x-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"16x%5E2-86x%2B30=2%28x-5%29%288x-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"2%28x-5%29%288x-3%29\"$ to get $\"16x%5E2-86x%2B30\"$ 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, you can email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "To find other ways to contact me, you can also visit my website: http://www.freewebs.com/jimthompson5910/home.html\r
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\n" ); document.write( "\n" ); document.write( "Thanks,\r
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\n" ); document.write( "\n" ); document.write( "Jim\r
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