document.write( "Question 366639: I'm having some trouble with factoring Polynomials with a coefficient in front of the squared variable. 10r2-25r-6. I've tried (2r+2)(5r-3). \n" ); document.write( "

Algebra.Com's Answer #261288 by jim_thompson5910(35256) $\"\"$ $\"About$

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Looking at $\"10r%5E2-25r-6\"$ we can see that the first term is $\"10r%5E2\"$ and the last term is $\"-6\"$ where the coefficients are 10 and -6 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 10 and the last coefficient -6 to get -60. Now what two numbers multiply to -60 and add to the middle coefficient -25? Let's list all of the factors of -60:\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
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...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 -60\r
\n" ); document.write( "\n" ); document.write( "(1)*(-60)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-30)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-15)\r
\n" ); document.write( "\n" ); document.write( "(5)*(-12)\r
\n" ); document.write( "\n" ); document.write( "(6)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(60)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(30)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(20)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(15)\r
\n" ); document.write( "\n" ); document.write( "(-5)*(12)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(10)\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 -25? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -25\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( "None of these pairs of factors add to -25. So the expression $\"10r%5E2-25r-6\"$ cannot be factored\r
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