document.write( "Question 147539This question is from textbook algebra
\n" ); document.write( ": It says to factor the problem. The problem is 4x^2+7x-2, the answer I got was 62(2x^2+6^2-1) I got it wrond though. Please help me Thank You=) \n" ); document.write( "

Algebra.Com's Answer #107910 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "\n" ); document.write( "Looking at $\"4x%5E2%2B7x-2\"$ we can see that the first term is $\"4x%5E2\"$ and the last term is $\"-2\"$ where the coefficients are 4 and -2 respectively.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 4 and the last coefficient -2 to get -8. Now what two numbers multiply to -8 and add to the middle coefficient 7? Let's list all of the factors of -8:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factors of -8:\r
\n" ); document.write( "\n" ); document.write( "1,2,4,8\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-8 ...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 -8\r
\n" ); document.write( "\n" ); document.write( "(1)*(-8)\r
\n" ); document.write( "\n" ); document.write( "(2)*(-4)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(8)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(4)\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 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

First Number	Second Number	Sum
1	-8	1+(-8)=-7
2	-4	2+(-4)=-2
-1	8	-1+8=7
-2	4	-2+4=2

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From this list we can see that -1 and 8 add up to 7 and multiply to -8\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"4x%5E2%2B7x-2\"$ , replace $\"7x\"$ with $\"-1x%2B8x\"$ (notice $\"-1x%2B8x\"$ adds up to $\"7x\"$ . So it is equivalent to $\"7x\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"4x%5E2%2Bhighlight%28-1x%2B8x%29%2B-2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's factor $\"4x%5E2-1x%2B8x-2\"$ by grouping:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%284x%5E2-1x%29%2B%288x-2%29\"$ Group like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x%284x-1%29%2B2%284x-1%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"2\"$ out of the second group\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%284x-1%29\"$ Since we have a common term of $\"4x-1\"$ , we can combine like terms\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2-1x%2B8x-2\"$ factors to $\"%28x%2B2%29%284x-1%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So this also means that $\"4x%5E2%2B7x-2\"$ factors to $\"%28x%2B2%29%284x-1%29\"$ (since $\"4x%5E2%2B7x-2\"$ is equivalent to $\"4x%5E2-1x%2B8x-2\"$ )\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 $\"4x%5E2%2B7x-2\"$ factors to $\"%28x%2B2%29%284x-1%29\"$
\n" ); document.write( " \n" ); document.write( "

\n" );