document.write( "Question 186943: please help me solve by factoring.
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\n" ); document.write( "4x^2-11x+6=0 and show work so i can do this on my own tomorrow. thanks
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Algebra.Com's Answer #140114 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, factor $\"4x%5E2-11x%2B6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"4x%5E2-11x%2B6\"$ , we can see that the first coefficient is $\"4\"$ , the second coefficient is $\"-11\"$ , and the last term is $\"6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"4\"$ by the last term $\"6\"$ to get $\"%284%29%286%29=24\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"24\"$ (the previous product) and add to the second coefficient $\"-11\"$ ?\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 $\"24\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"24\"$ :\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-8,-12,-24\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 $\"24\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*24
\n" ); document.write( "2*12
\n" ); document.write( "3*8
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\n" ); document.write( "(-1)*(-24)
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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 $\"-11\"$ :\r
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First Number	Second Number	Sum
1	24	1+24=25
2	12	2+12=14
3	8	3+8=11
4	6	4+6=10
-1	-24	-1+(-24)=-25
-2	-12	-2+(-12)=-14
-3	-8	-3+(-8)=-11
-4	-6	-4+(-6)=-10

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"-8\"$ add to $\"-11\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"-8\"$ both multiply to $\"24\"$ and add to $\"-11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"-11x\"$ with $\"-3x-8x\"$ . Remember, $\"-3\"$ and $\"-8\"$ add to $\"-11\"$ . So this shows us that $\"-3x-8x=-11x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E2%2Bhighlight%28-3x-8x%29%2B6\"$ Replace the second term $\"-11x\"$ with $\"-3x-8x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%284x%5E2-3x%29%2B%28-8x%2B6%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%284x-3%29%2B%28-8x%2B6%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%284x-3%29-2%284x-3%29\"$ 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( " $\"%28x-2%29%284x-3%29\"$ Combine like terms. Or factor out the common term $\"4x-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2-11x%2B6\"$ factors to $\"%28x-2%29%284x-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2-11x%2B6=0\"$ becomes $\"%28x-2%29%284x-3%29=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero (by the use of the zero product property):\r
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\n" ); document.write( "\n" ); document.write( " $\"x-2=0\"$ or $\"4x-3=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=2\"$ or $\"x=3%2F4\"$ Now solve for x in each case\r
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\n" ); document.write( "\n" ); document.write( "So the solutions are\r
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\n" ); document.write( "\n" ); document.write( " $\"x=2\"$ or $\"x=3%2F4\"$ \n" ); document.write( "

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