document.write( "Question 183160This question is from textbook
\n" ); document.write( ": 6g^3-24g^2+24g \n" ); document.write( "

Algebra.Com's Answer #137533 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I assume that you want to factor right? Please post full instructions.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"6g%5E3-24g%5E2%2B24g\"$ Start with the given expression\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"6g%28g%5E2-4g%2B4%29\"$ Factor out the GCF $\"6g\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"g%5E2-4g%2B4\"$ \r
\n" ); document.write( "
\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( "Looking at $\"1g%5E2-4g%2B4\"$ we can see that the first term is $\"1g%5E2\"$ and the last term is $\"4\"$ where the coefficients are 1 and 4 respectively.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 4 to get 4. Now what two numbers multiply to 4 and add to the middle coefficient -4? Let's list all of the factors of 4:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factors of 4:\r
\n" ); document.write( "\n" ); document.write( "1,2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-1,-2 ...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 4\r
\n" ); document.write( "\n" ); document.write( "1*4\r
\n" ); document.write( "\n" ); document.write( "2*2\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-4)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-2)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

First Number	Second Number	Sum
1	4	1+4=5
2	2	2+2=4
-1	-4	-1+(-4)=-5
-2	-2	-2+(-2)=-4

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "From this list we can see that -2 and -2 add up to -4 and multiply to 4\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1g%5E2-4g%2B4\"$ , replace $\"-4g\"$ with $\"-2g%2B-2g\"$ (notice $\"-2g%2B-2g\"$ adds up to $\"-4g\"$ . So it is equivalent to $\"-4g\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"1g%5E2%2Bhighlight%28-2g%2B-2g%29%2B4\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1g%5E2-2g-2g%2B4\"$ by grouping:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%281g%5E2-2g%29%2B%28-2g%2B4%29\"$ Group like terms\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"g%28g-2%29-2%28g-2%29\"$ Factor out the GCF of $\"g\"$ 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( " $\"%28g-2%29%28g-2%29\"$ Since we have a common term of $\"g-2\"$ , we can combine like terms\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"1g%5E2-2g-2g%2B4\"$ factors to $\"%28g-2%29%28g-2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So this also means that $\"1g%5E2-4g%2B4\"$ factors to $\"%28g-2%29%28g-2%29\"$ (since $\"1g%5E2-4g%2B4\"$ is equivalent to $\"1g%5E2-2g-2g%2B4\"$ )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "note: $\"%28g-2%29%28g-2%29\"$ is equivalent to $\"%28g-2%29%5E2\"$ since the term $\"g-2\"$ occurs twice. So $\"1g%5E2-4g%2B4\"$ also factors to $\"%28g-2%29%5E2\"$ \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( "\n" ); document.write( "So our expression goes from $\"6g%28g%5E2-4g%2B4%29\"$ and factors further to $\"6g%28g-2%29%5E2\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So $\"6g%5E3-24g%5E2%2B24g\"$ factors to $\"6g%28g-2%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );