document.write( "Question 725344: I'm having a problem in figuring out what the \"2\" in front of 2x(squared) means.
\n" ); document.write( "This is factoring polynomials mentally or with the box method.\r
\n" ); document.write( "\n" ); document.write( "2x(squared) + 11x - 21\r
\n" ); document.write( "\n" ); document.write( "The missing numbers are -3 and 14.\r
\n" ); document.write( "\n" ); document.write( "I know I'm supposed to multiply -21 by 2, but what do I do after solving for the two missing numbers? \n" ); document.write( "

Algebra.Com's Answer #444106 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Looking at the expression $\"2x%5E2%2B11x-21\"$ , we can see that the first coefficient is $\"2\"$ , the second coefficient is $\"11\"$ , and the last term is $\"-21\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"2\"$ by the last term $\"-21\"$ to get $\"%282%29%28-21%29=-42\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-42\"$ (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 $\"-42\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-42\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,2,3,6,7,14,21,42\r
\n" ); document.write( "\n" ); document.write( "-1,-2,-3,-6,-7,-14,-21,-42\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 $\"-42\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-42) = -42
\n" ); document.write( "2*(-21) = -42
\n" ); document.write( "3*(-14) = -42
\n" ); document.write( "6*(-7) = -42
\n" ); document.write( "(-1)*(42) = -42
\n" ); document.write( "(-2)*(21) = -42
\n" ); document.write( "(-3)*(14) = -42
\n" ); document.write( "(-6)*(7) = -42\r
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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	-42	1+(-42)=-41
2	-21	2+(-21)=-19
3	-14	3+(-14)=-11
6	-7	6+(-7)=-1
-1	42	-1+42=41
-2	21	-2+21=19
-3	14	-3+14=11
-6	7	-6+7=1

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-3\"$ and $\"14\"$ add to $\"11\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-3\"$ and $\"14\"$ both multiply to $\"-42\"$ and add to $\"11\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"11x\"$ with $\"-3x%2B14x\"$ . Remember, $\"-3\"$ and $\"14\"$ add to $\"11\"$ . So this shows us that $\"-3x%2B14x=11x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"2x%5E2%2Bhighlight%28-3x%2B14x%29-21\"$ Replace the second term $\"11x\"$ with $\"-3x%2B14x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%282x%5E2-3x%29%2B%2814x-21%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x-3%29%2B%2814x-21%29\"$ Factor out the GCF $\"x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"x%282x-3%29%2B7%282x-3%29\"$ Factor out $\"7\"$ 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( " $\"%28x%2B7%29%282x-3%29\"$ Combine like terms. Or factor out the common term $\"2x-3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"2x%5E2%2B11x-21\"$ factors to $\"%28x%2B7%29%282x-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"2x%5E2%2B11x-21=%28x%2B7%29%282x-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%28x%2B7%29%282x-3%29\"$ to get $\"2x%5E2%2B11x-21\"$ or by graphing the original expression and the answer (the two graphs should be identical).
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