document.write( "Question 114220: Factor completely.\r
\n" ); document.write( "\n" ); document.write( "14x squared - 20x + 6 \n" ); document.write( "

Algebra.Com's Answer #83626 by jim_thompson5910(35256) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Looking at $\"14x%5E2-20x%2B6\"$ we can see that the first term is $\"14x%5E2\"$ and the last term is $\"6\"$ where the coefficients are 14 and 6 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 14 and the last coefficient 6 to get 84. Now what two numbers multiply to 84 and add to the middle coefficient -20? Let's list all of the factors of 84:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 84:\r
\n" ); document.write( "\n" ); document.write( "1,2,3,4,6,7,12,14,21,28,42,84\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-4,-6,-7,-12,-14,-21,-28,-42,-84 ...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 84\r
\n" ); document.write( "\n" ); document.write( "1*84\r
\n" ); document.write( "\n" ); document.write( "2*42\r
\n" ); document.write( "\n" ); document.write( "3*28\r
\n" ); document.write( "\n" ); document.write( "4*21\r
\n" ); document.write( "\n" ); document.write( "6*14\r
\n" ); document.write( "\n" ); document.write( "7*12\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-84)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-42)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-28)\r
\n" ); document.write( "\n" ); document.write( "(-4)*(-21)\r
\n" ); document.write( "\n" ); document.write( "(-6)*(-14)\r
\n" ); document.write( "\n" ); document.write( "(-7)*(-12)\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 -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20\r
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First Number	Second Number	Sum
1	84	1+84=85
2	42	2+42=44
3	28	3+28=31
4	21	4+21=25
6	14	6+14=20
7	12	7+12=19
-1	-84	-1+(-84)=-85
-2	-42	-2+(-42)=-44
-3	-28	-3+(-28)=-31
-4	-21	-4+(-21)=-25
-6	-14	-6+(-14)=-20
-7	-12	-7+(-12)=-19

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -6 and -14 add up to -20 and multiply to 84\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"14x%5E2-20x%2B6\"$ , replace $\"-20x\"$ with $\"-6x%2B-14x\"$ (notice $\"-6x%2B-14x\"$ adds up to $\"-20x\"$ . So it is equivalent to $\"-20x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"14x%5E2%2Bhighlight%28-6x%2B-14x%29%2B6\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"14x%5E2-6x-14x%2B6\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%2814x%5E2-6x%29%2B%28-14x%2B6%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%287x-3%29-2%287x-3%29\"$ Factor out the GCF of $\"2x\"$ out of the first group. Factor out the GCF of $\"-2\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x-2%29%287x-3%29\"$ Since we have a common term of $\"7x-3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"14x%5E2-6x-14x%2B6\"$ factors to $\"%282x-2%29%287x-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"14x%5E2-20x%2B6\"$ factors to $\"%282x-2%29%287x-3%29\"$ (since $\"14x%5E2-20x%2B6\"$ is equivalent to $\"14x%5E2-6x-14x%2B6\"$ )
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