document.write( "Question 336721: What is the factorization of 20xsquared+27x-8 \n" ); document.write( "

Algebra.Com's Answer #241362 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"20x%5E2%2B27x-8\"$ we can see that the first term is $\"20x%5E2\"$ and the last term is $\"-8\"$ where the coefficients are 20 and -8 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 20 and the last coefficient -8 to get -160. Now what two numbers multiply to -160 and add to the middle coefficient 27? Let's list all of the factors of -160:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -160:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,8,10,16,20,32,40,80,160\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-8,-10,-16,-20,-32,-40,-80,-160 ...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 -160\r
\n" ); document.write( "\n" ); document.write( "(1)*(-160)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-80)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-40)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-32)\r
\n" ); document.write( "\n" ); document.write( "(8)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(10)*(-16)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(160)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(80)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(40)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(32)\r
\n" ); document.write( "\n" ); document.write( "(-8)*(20)\r
\n" ); document.write( "\n" ); document.write( "(-10)*(16)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 27? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 27\r
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First Number	Second Number	Sum
1	-160	1+(-160)=-159
2	-80	2+(-80)=-78
4	-40	4+(-40)=-36
5	-32	5+(-32)=-27
8	-20	8+(-20)=-12
10	-16	10+(-16)=-6
-1	160	-1+160=159
-2	80	-2+80=78
-4	40	-4+40=36
-5	32	-5+32=27
-8	20	-8+20=12
-10	16	-10+16=6

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -5 and 32 add up to 27 and multiply to -160\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"20x%5E2%2B27x-8\"$ , replace $\"27x\"$ with $\"-5x%2B32x\"$ (notice $\"-5x%2B32x\"$ adds up to $\"27x\"$ . So it is equivalent to $\"27x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"20x%5E2%2Bhighlight%28-5x%2B32x%29%2B-8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"20x%5E2-5x%2B32x-8\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2820x%5E2-5x%29%2B%2832x-8%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%284x-1%29%2B8%284x-1%29\"$ Factor out the GCF of $\"5x\"$ out of the first group. Factor out the GCF of $\"8\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%285x%2B8%29%284x-1%29\"$ Since we have a common term of $\"4x-1\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"20x%5E2-5x%2B32x-8\"$ factors to $\"%285x%2B8%29%284x-1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"20x%5E2%2B27x-8\"$ factors to $\"%285x%2B8%29%284x-1%29\"$ (since $\"20x%5E2%2B27x-8\"$ is equivalent to $\"20x%5E2-5x%2B32x-8\"$ )\r
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\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"20x%5E2%2B27x-8\"$ factors to $\"%285x%2B8%29%284x-1%29\"$ \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, feel free to check out my website. \r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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