document.write( "Question 191478: 50x^3+95x^2+30x\r
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Algebra.Com's Answer #143676 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"50x%5E3%2B95x%5E2%2B30x\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"5x%2810x%5E2%2B19x%2B6%29\"$ Factor out the GCF $\"5x\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"10x%5E2%2B19x%2B6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"10x%5E2%2B19x%2B6\"$ we can see that the first term is $\"10x%5E2\"$ 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 19? 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 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 19? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 19\r
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First Number	Second Number	Sum
1	60	1+60=61
2	30	2+30=32
3	20	3+20=23
4	15	4+15=19
5	12	5+12=17
6	10	6+10=16
-1	-60	-1+(-60)=-61
-2	-30	-2+(-30)=-32
-3	-20	-3+(-20)=-23
-4	-15	-4+(-15)=-19
-5	-12	-5+(-12)=-17
-6	-10	-6+(-10)=-16

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 4 and 15 add up to 19 and multiply to 60\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"10x%5E2%2B19x%2B6\"$ , replace $\"19x\"$ with $\"4x%2B15x\"$ (notice $\"4x%2B15x\"$ adds up to $\"19x\"$ . So it is equivalent to $\"19x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"10x%5E2%2Bhighlight%284x%2B15x%29%2B6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"10x%5E2%2B4x%2B15x%2B6\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2810x%5E2%2B4x%29%2B%2815x%2B6%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%285x%2B2%29%2B3%285x%2B2%29\"$ Factor out the GCF of $\"2x\"$ out of the first group. Factor out the GCF of $\"3\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%2B3%29%285x%2B2%29\"$ Since we have a common term of $\"5x%2B2\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"10x%5E2%2B4x%2B15x%2B6\"$ factors to $\"%282x%2B3%29%285x%2B2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"10x%5E2%2B19x%2B6\"$ factors to $\"%282x%2B3%29%285x%2B2%29\"$ (since $\"10x%5E2%2B19x%2B6\"$ is equivalent to $\"10x%5E2%2B4x%2B15x%2B6\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"5x%2810x%5E2%2B19x%2B6%29\"$ and factors further to $\"5x%282x%2B3%29%285x%2B2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"50x%5E3%2B95x%5E2%2B30x\"$ completely factors to $\"5x%282x%2B3%29%285x%2B2%29\"$ \r
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