document.write( "Question 336804: Can you please help me factor this polynomial?\r
\n" ); document.write( "\n" ); document.write( "8x^2 + 16x +12 thank you! \n" ); document.write( "

Algebra.Com's Answer #241412 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"8x%5E2%2B16x%2B12\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"4%282x%5E2%2B4x%2B3%29\"$ Factor out the GCF $\"4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"2x%5E2%2B4x%2B3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"2x%5E2%2B4x%2B3\"$ we can see that the first term is $\"2x%5E2\"$ and the last term is $\"3\"$ where the coefficients are 2 and 3 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 2 and the last coefficient 3 to get 6. Now what two numbers multiply to 6 and add to the middle coefficient 4? Let's list all of the factors of 6:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 6:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6 ...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 6\r
\n" ); document.write( "\n" ); document.write( "1*6\r
\n" ); document.write( "\n" ); document.write( "2*3\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-6)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-3)\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 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4\r
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First Number	Second Number	Sum
1	6	1+6=7
2	3	2+3=5
-1	-6	-1+(-6)=-7
-2	-3	-2+(-3)=-5

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\n" ); document.write( "\n" ); document.write( "None of these pairs of factors add to 4. So the expression $\"2x%5E2%2B4x%2B3\"$ cannot be factored\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"8x%5E2%2B16x%2B12\"$ factors to $\"4%282x%5E2%2B4x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my website. \r
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\n" ); document.write( "\n" ); document.write( "Jim
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