document.write( "Question 887717: please factor it!!!?
\n" ); document.write( "8x square + 5x - 200=0
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Algebra.Com's Answer #536814 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 $\"8x%5E2%2B5x-200\"$ , we can see that the first coefficient is $\"8\"$ , the second coefficient is $\"5\"$ , and the last term is $\"-200\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"8\"$ by the last term $\"-200\"$ to get $\"%288%29%28-200%29=-1600\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-1600\"$ (the previous product) and add to the second coefficient $\"5\"$ ?\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 $\"-1600\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-1600\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,160,200,320,400,800,1600\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-8,-10,-16,-20,-25,-32,-40,-50,-64,-80,-100,-160,-200,-320,-400,-800,-1600\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 $\"-1600\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-1600) = -1600
\n" ); document.write( "2*(-800) = -1600
\n" ); document.write( "4*(-400) = -1600
\n" ); document.write( "5*(-320) = -1600
\n" ); document.write( "8*(-200) = -1600
\n" ); document.write( "10*(-160) = -1600
\n" ); document.write( "16*(-100) = -1600
\n" ); document.write( "20*(-80) = -1600
\n" ); document.write( "25*(-64) = -1600
\n" ); document.write( "32*(-50) = -1600
\n" ); document.write( "40*(-40) = -1600
\n" ); document.write( "(-1)*(1600) = -1600
\n" ); document.write( "(-2)*(800) = -1600
\n" ); document.write( "(-4)*(400) = -1600
\n" ); document.write( "(-5)*(320) = -1600
\n" ); document.write( "(-8)*(200) = -1600
\n" ); document.write( "(-10)*(160) = -1600
\n" ); document.write( "(-16)*(100) = -1600
\n" ); document.write( "(-20)*(80) = -1600
\n" ); document.write( "(-25)*(64) = -1600
\n" ); document.write( "(-32)*(50) = -1600
\n" ); document.write( "(-40)*(40) = -1600\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 $\"5\"$ :\r
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First Number	Second Number	Sum
1	-1600	1+(-1600)=-1599
2	-800	2+(-800)=-798
4	-400	4+(-400)=-396
5	-320	5+(-320)=-315
8	-200	8+(-200)=-192
10	-160	10+(-160)=-150
16	-100	16+(-100)=-84
20	-80	20+(-80)=-60
25	-64	25+(-64)=-39
32	-50	32+(-50)=-18
40	-40	40+(-40)=0
-1	1600	-1+1600=1599
-2	800	-2+800=798
-4	400	-4+400=396
-5	320	-5+320=315
-8	200	-8+200=192
-10	160	-10+160=150
-16	100	-16+100=84
-20	80	-20+80=60
-25	64	-25+64=39
-32	50	-32+50=18
-40	40	-40+40=0

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that there are no pairs of numbers which add to $\"5\"$ . So $\"8x%5E2%2B5x-200\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"8x%5E2%2B5x-200\"$ doesn't factor at all (over the rational numbers).\r
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\n" ); document.write( "\n" ); document.write( "So $\"8x%5E2%2B5x-200\"$ is prime.\r
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\n" ); document.write( "\n" ); document.write( "To solve $\"8x%5E2%2B5x-200=0\"$ you need to use the quadratic equation. \n" ); document.write( "

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