document.write( "Question 635651: What are the x factors of this quadratic equation 5x^2+2x+10=0.
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Algebra.Com's Answer #400458 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"5x%5E2%2B2x%2B10\"$ , we can see that the first coefficient is $\"5\"$ , the second coefficient is $\"2\"$ , and the last term is $\"10\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"5\"$ by the last term $\"10\"$ to get $\"%285%29%2810%29=50\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"50\"$ (the previous product) and add to the second coefficient $\"2\"$ ?\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 $\"50\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"50\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-5,-10,-25,-50\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 $\"50\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*50 = 50
\n" ); document.write( "2*25 = 50
\n" ); document.write( "5*10 = 50
\n" ); document.write( "(-1)*(-50) = 50
\n" ); document.write( "(-2)*(-25) = 50
\n" ); document.write( "(-5)*(-10) = 50\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 $\"2\"$ :\r
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First Number	Second Number	Sum
1	50	1+50=51
2	25	2+25=27
5	10	5+10=15
-1	-50	-1+(-50)=-51
-2	-25	-2+(-25)=-27
-5	-10	-5+(-10)=-15

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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 $\"2\"$ . So $\"5x%5E2%2B2x%2B10\"$ cannot be factored.\r
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\n" ); document.write( "\n" ); document.write( "So $\"5x%5E2%2B2x%2B10\"$ doesn't factor at all (over the rational numbers).\r
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\n" ); document.write( "\n" ); document.write( "So $\"5x%5E2%2B2x%2B10\"$ is prime.\r
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\n" ); document.write( "\n" ); document.write( "So the best way to solve the original equation is to use the quadratic formula. Let me know if you need help solving using the quadratic formula.\r
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