document.write( "Question 186951: please solve by factoring...i got stuck near the end.
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\n" ); document.write( "3x^2+8x+4=0
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\n" ); document.write( "thanks \n" ); document.write( "

Algebra.Com's Answer #140118 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's factor $\"3x%5E2%2B8x%2B4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"3x%5E2%2B8x%2B4\"$ , we can see that the first coefficient is $\"3\"$ , the second coefficient is $\"8\"$ , and the last term is $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"3\"$ by the last term $\"4\"$ to get $\"%283%29%284%29=12\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"12\"$ (the previous product) and add to the second coefficient $\"8\"$ ?\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 $\"12\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"12\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-12\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 $\"12\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*12
\n" ); document.write( "2*6
\n" ); document.write( "3*4
\n" ); document.write( "(-1)*(-12)
\n" ); document.write( "(-2)*(-6)
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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 $\"8\"$ :\r
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First Number	Second Number	Sum
1	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"2\"$ and $\"6\"$ add to $\"8\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"2\"$ and $\"6\"$ both multiply to $\"12\"$ and add to $\"8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"8x\"$ with $\"2x%2B6x\"$ . Remember, $\"2\"$ and $\"6\"$ add to $\"8\"$ . So this shows us that $\"2x%2B6x=8x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2%2Bhighlight%282x%2B6x%29%2B4\"$ Replace the second term $\"8x\"$ with $\"2x%2B6x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x%5E2%2B2x%29%2B%286x%2B4%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x%2B2%29%2B%286x%2B4%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%283x%2B2%29%2B2%283x%2B2%29\"$ Factor out $\"2\"$ from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%283x%2B2%29\"$ Combine like terms. Or factor out the common term $\"3x%2B2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B8x%2B4\"$ factors to $\"%28x%2B2%29%283x%2B2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So $\"3x%5E2%2B8x%2B4=0\"$ then transforms to $\"%28x%2B2%29%283x%2B2%29=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( " $\"x%2B2=0\"$ or $\"3x%2B2=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=-2\"$ or $\"x=-2%2F3\"$ Solve for x in each case\r
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\n" ); document.write( "\n" ); document.write( "So our answers are \r
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\n" ); document.write( "\n" ); document.write( " $\"x=-2\"$ or $\"x=-2%2F3\"$ \n" ); document.write( "

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