document.write( "Question 538903: Please help me factor $\"+9x%5E2%2B89x%2B40+\"$
\n" ); document.write( "I know that the first number in the bracket will probably have to be 9 or 3 but I'm not sure about how about the other numbers since 89 and 40 do not have a common multiple.
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Algebra.Com's Answer #353279 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Looking at the expression $\"9x%5E2%2B89x%2B40\"$ , we can see that the first coefficient is $\"9\"$ , the second coefficient is $\"89\"$ , and the last term is $\"40\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"9\"$ by the last term $\"40\"$ to get $\"%289%29%2840%29=360\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"360\"$ (the previous product) and add to the second coefficient $\"89\"$ ?\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 $\"360\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"360\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-8,-9,-10,-12,-15,-18,-20,-24,-30,-36,-40,-45,-60,-72,-90,-120,-180,-360\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 $\"360\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*360 = 360
\n" ); document.write( "2*180 = 360
\n" ); document.write( "3*120 = 360
\n" ); document.write( "4*90 = 360
\n" ); document.write( "5*72 = 360
\n" ); document.write( "6*60 = 360
\n" ); document.write( "8*45 = 360
\n" ); document.write( "9*40 = 360
\n" ); document.write( "10*36 = 360
\n" ); document.write( "12*30 = 360
\n" ); document.write( "15*24 = 360
\n" ); document.write( "18*20 = 360
\n" ); document.write( "(-1)*(-360) = 360
\n" ); document.write( "(-2)*(-180) = 360
\n" ); document.write( "(-3)*(-120) = 360
\n" ); document.write( "(-4)*(-90) = 360
\n" ); document.write( "(-5)*(-72) = 360
\n" ); document.write( "(-6)*(-60) = 360
\n" ); document.write( "(-8)*(-45) = 360
\n" ); document.write( "(-9)*(-40) = 360
\n" ); document.write( "(-10)*(-36) = 360
\n" ); document.write( "(-12)*(-30) = 360
\n" ); document.write( "(-15)*(-24) = 360
\n" ); document.write( "(-18)*(-20) = 360\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 $\"89\"$ :\r
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First Number	Second Number	Sum
1	360	1+360=361
2	180	2+180=182
3	120	3+120=123
4	90	4+90=94
5	72	5+72=77
6	60	6+60=66
8	45	8+45=53
9	40	9+40=49
10	36	10+36=46
12	30	12+30=42
15	24	15+24=39
18	20	18+20=38
-1	-360	-1+(-360)=-361
-2	-180	-2+(-180)=-182
-3	-120	-3+(-120)=-123
-4	-90	-4+(-90)=-94
-5	-72	-5+(-72)=-77
-6	-60	-6+(-60)=-66
-8	-45	-8+(-45)=-53
-9	-40	-9+(-40)=-49
-10	-36	-10+(-36)=-46
-12	-30	-12+(-30)=-42
-15	-24	-15+(-24)=-39
-18	-20	-18+(-20)=-38

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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 $\"89\"$ . So $\"9x%5E2%2B89x%2B40\"$ 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 $\"9x%5E2%2B89x%2B40\"$ doesn't factor at all (over the rational numbers).\r
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\n" ); document.write( "\n" ); document.write( "So $\"9x%5E2%2B89x%2B40\"$ is prime.\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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\n" ); document.write( "\n" ); document.write( "Jim
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