document.write( "Question 539493: THE factor polynomial problem is 15x2−84x−36\r
\n" ); document.write( "\n" ); document.write( "I know the answer to the polynomial is 3(5x+2)(x−6)but i dont understand how you get from \r
\n" ); document.write( "\n" ); document.write( "3(5x2−28x−12)to 3(5x+2)(x−6)<----the answer\r
\n" ); document.write( "\n" ); document.write( "can you please show me how you get it STEP BY STEP\r
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Algebra.Com's Answer #353432 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"15x%5E2-84x-36\"$ Start with the given expression.\r
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\n" ); document.write( "\n" ); document.write( " $\"3%285x%5E2-28x-12%29\"$ Factor out the GCF $\"3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's try to factor the inner expression $\"5x%5E2-28x-12\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"5x%5E2-28x-12\"$ , we can see that the first coefficient is $\"5\"$ , the second coefficient is $\"-28\"$ , and the last term is $\"-12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"5\"$ by the last term $\"-12\"$ to get $\"%285%29%28-12%29=-60\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-60\"$ (the previous product) and add to the second coefficient $\"-28\"$ ?\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 $\"-60\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-60\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,10,12,15,20,30,60\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60\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 $\"-60\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-60) = -60
\n" ); document.write( "2*(-30) = -60
\n" ); document.write( "3*(-20) = -60
\n" ); document.write( "4*(-15) = -60
\n" ); document.write( "5*(-12) = -60
\n" ); document.write( "6*(-10) = -60
\n" ); document.write( "(-1)*(60) = -60
\n" ); document.write( "(-2)*(30) = -60
\n" ); document.write( "(-3)*(20) = -60
\n" ); document.write( "(-4)*(15) = -60
\n" ); document.write( "(-5)*(12) = -60
\n" ); document.write( "(-6)*(10) = -60\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 $\"-28\"$ :\r
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First Number	Second Number	Sum
1	-60	1+(-60)=-59
2	-30	2+(-30)=-28
3	-20	3+(-20)=-17
4	-15	4+(-15)=-11
5	-12	5+(-12)=-7
6	-10	6+(-10)=-4
-1	60	-1+60=59
-2	30	-2+30=28
-3	20	-3+20=17
-4	15	-4+15=11
-5	12	-5+12=7
-6	10	-6+10=4

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"2\"$ and $\"-30\"$ add to $\"-28\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"2\"$ and $\"-30\"$ both multiply to $\"-60\"$ and add to $\"-28\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-28x\"$ with $\"2x-30x\"$ . Remember, $\"2\"$ and $\"-30\"$ add to $\"-28\"$ . So this shows us that $\"2x-30x=-28x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%5E2%2Bhighlight%282x-30x%29-12\"$ Replace the second term $\"-28x\"$ with $\"2x-30x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%285x%5E2%2B2x%29%2B%28-30x-12%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%285x%2B2%29%2B%28-30x-12%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%285x%2B2%29-6%285x%2B2%29\"$ Factor out $\"6\"$ 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( " $\"%28x-6%29%285x%2B2%29\"$ Combine like terms. Or factor out the common term $\"5x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"3%285x%5E2-28x-12%29\"$ then factors further to $\"3%28x-6%29%285x%2B2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"15x%5E2-84x-36\"$ completely factors to $\"3%28x-6%29%285x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"15x%5E2-84x-36=3%28x-6%29%285x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"3%28x-6%29%285x%2B2%29\"$ to get $\"15x%5E2-84x-36\"$ 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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