document.write( "Question 171902This question is from textbook
\n" ); document.write( ": x^4-20x^3+96x^2 could you help me solve this problem on factoring trinomials. \n" ); document.write( "

Algebra.Com's Answer #126994 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"x%5E4-20x%5E3%2B96x%5E2\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28x%5E2-20x%2B96%29\"$ Factor out the GCF $\"x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"x%5E2-20x%2B96\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"1x%5E2-20x%2B96\"$ we can see that the first term is $\"1x%5E2\"$ and the last term is $\"96\"$ where the coefficients are 1 and 96 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 96 to get 96. Now what two numbers multiply to 96 and add to the middle coefficient -20? Let's list all of the factors of 96:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 96:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,8,12,16,24,32,48,96\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-16,-24,-32,-48,-96 ...List the negative factors as well. 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 96\r
\n" ); document.write( "\n" ); document.write( "1*96\r
\n" ); document.write( "\n" ); document.write( "2*48\r
\n" ); document.write( "\n" ); document.write( "3*32\r
\n" ); document.write( "\n" ); document.write( "4*24\r
\n" ); document.write( "\n" ); document.write( "6*16\r
\n" ); document.write( "\n" ); document.write( "8*12\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-96)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-48)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-32)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-24)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(-12)\r
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\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20\r
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First Number	Second Number	Sum
1	96	1+96=97
2	48	2+48=50
3	32	3+32=35
4	24	4+24=28
6	16	6+16=22
8	12	8+12=20
-1	-96	-1+(-96)=-97
-2	-48	-2+(-48)=-50
-3	-32	-3+(-32)=-35
-4	-24	-4+(-24)=-28
-6	-16	-6+(-16)=-22
-8	-12	-8+(-12)=-20

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -8 and -12 add up to -20 and multiply to 96\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1x%5E2-20x%2B96\"$ , replace $\"-20x\"$ with $\"-8x%2B-12x\"$ (notice $\"-8x%2B-12x\"$ adds up to $\"-20x\"$ . So it is equivalent to $\"-20x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1x%5E2%2Bhighlight%28-8x%2B-12x%29%2B96\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1x%5E2-8x-12x%2B96\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281x%5E2-8x%29%2B%28-12x%2B96%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%28x-8%29-12%28x-8%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-12\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-12%29%28x-8%29\"$ Since we have a common term of $\"x-8\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1x%5E2-8x-12x%2B96\"$ factors to $\"%28x-12%29%28x-8%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1x%5E2-20x%2B96\"$ factors to $\"%28x-12%29%28x-8%29\"$ (since $\"1x%5E2-20x%2B96\"$ is equivalent to $\"1x%5E2-8x-12x%2B96\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"x%5E2%28x%5E2-20x%2B96%29\"$ and factors further to $\"x%5E2%28x-12%29%28x-8%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"x%5E4-20x%5E3%2B96x%5E2\"$ factors to $\"x%5E2%28x-12%29%28x-8%29\"$ \r
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