document.write( "Question 143267: 4x2 + 34x + 42
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Algebra.Com's Answer #104253 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Do you want to factor?\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E2%2B34x%2B42\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"2%282x%5E2%2B17x%2B21%29\"$ Factor out the GCF $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"2x%5E2%2B17x%2B21\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"2x%5E2%2B17x%2B21\"$ we can see that the first term is $\"2x%5E2\"$ and the last term is $\"21\"$ where the coefficients are 2 and 21 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 2 and the last coefficient 21 to get 42. Now what two numbers multiply to 42 and add to the middle coefficient 17? Let's list all of the factors of 42:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 42:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-7,-14,-21,-42 ...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 42\r
\n" ); document.write( "\n" ); document.write( "1*42\r
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\n" ); document.write( "\n" ); document.write( "3*14\r
\n" ); document.write( "\n" ); document.write( "6*7\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-42)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-21)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(-14)\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 17? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 17\r
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First Number	Second Number	Sum
1	42	1+42=43
2	21	2+21=23
3	14	3+14=17
6	7	6+7=13
-1	-42	-1+(-42)=-43
-2	-21	-2+(-21)=-23
-3	-14	-3+(-14)=-17
-6	-7	-6+(-7)=-13

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\n" ); document.write( "\n" ); document.write( "From this list we can see that 3 and 14 add up to 17 and multiply to 42\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"2x%5E2%2B17x%2B21\"$ , replace $\"17x\"$ with $\"3x%2B14x\"$ (notice $\"3x%2B14x\"$ adds up to $\"17x\"$ . So it is equivalent to $\"17x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2Bhighlight%283x%2B14x%29%2B21\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"2x%5E2%2B3x%2B14x%2B21\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2%2B3x%29%2B%2814x%2B21%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x%2B3%29%2B7%282x%2B3%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"7\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x%2B7%29%282x%2B3%29\"$ Since we have a common term of $\"2x%2B3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2%2B3x%2B14x%2B21\"$ factors to $\"%28x%2B7%29%282x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"2x%5E2%2B17x%2B21\"$ factors to $\"%28x%2B7%29%282x%2B3%29\"$ (since $\"2x%5E2%2B17x%2B21\"$ is equivalent to $\"2x%5E2%2B3x%2B14x%2B21\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"2%282x%5E2%2B17x%2B21%29\"$ and factors further to $\"2%28x%2B7%29%282x%2B3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"4x%5E2%2B34x%2B42\"$ factors to $\"2%28x%2B7%29%282x%2B3%29\"$ \r
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