document.write( "Question 368608: 2x^2-x-10 \n" ); document.write( "

Algebra.Com's Answer #262654 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming you want to factor.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Looking at $\"2x%5E2-x-10\"$ we can see that the first term is $\"2x%5E2\"$ and the last term is $\"-10\"$ where the coefficients are 2 and -10 respectively.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 2 and the last coefficient -10 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient -1? Let's list all of the factors of -20:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factors of -20:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,5,10,20\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "These factors pair up and multiply to -20\r
\n" ); document.write( "\n" ); document.write( "(1)*(-20)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-10)\r
\n" ); document.write( "\n" ); document.write( "(4)*(-5)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(20)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(10)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(5)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

First Number	Second Number	Sum
1	-20	1+(-20)=-19
2	-10	2+(-10)=-8
4	-5	4+(-5)=-1
-1	20	-1+20=19
-2	10	-2+10=8
-4	5	-4+5=1

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From this list we can see that 4 and -5 add up to -1 and multiply to -20\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"2x%5E2-x-10\"$ , replace $\"-x\"$ with $\"4x%2B-5x\"$ (notice $\"4x%2B-5x\"$ adds up to $\"-x\"$ . So it is equivalent to $\"-x\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2Bhighlight%284x%2B-5x%29%2B-10\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's factor $\"2x%5E2%2B4x-5x-10\"$ by grouping:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2%2B4x%29%2B%28-5x-10%29\"$ Group like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2x%28x%2B2%29-5%28x%2B2%29\"$ Factor out the GCF of $\"2x\"$ out of the first group. Factor out the GCF of $\"-5\"$ out of the second group\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%282x-5%29%28x%2B2%29\"$ Since we have a common term of $\"x%2B2\"$ , we can combine like terms\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2%2B4x-5x-10\"$ factors to $\"%282x-5%29%28x%2B2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So this also means that $\"2x%5E2-x-10\"$ factors to $\"%282x-5%29%28x%2B2%29\"$ (since $\"2x%5E2-x-10\"$ is equivalent to $\"2x%5E2%2B4x-5x-10\"$ )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2-x-10\"$ factors to $\"%282x-5%29%28x%2B2%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );