document.write( "Question 380373: I have a problem I need worked out and I do not understand it. I need it step by step please. It is factor each trinomial using the ac method. I hope someone can help me.\r
\n" ); document.write( "\n" ); document.write( "21x^2+2x-3\r
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Algebra.Com's Answer #270026 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 $\"21x%5E2%2B2x-3\"$ , we can see that the first coefficient is $\"21\"$ , the second coefficient is $\"2\"$ , and the last term is $\"-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient $\"21\"$ by the last term $\"-3\"$ to get $\"%2821%29%28-3%29=-63\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now the question is: what two whole numbers multiply to $\"-63\"$ (the previous product) and add to the second coefficient $\"2\"$ ?\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 $\"-63\"$ (the previous product).\r
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\n" ); document.write( "\n" ); document.write( "Factors of $\"-63\"$ :\r
\n" ); document.write( "\n" ); document.write( "1,3,7,9,21,63\r
\n" ); document.write( "\n" ); document.write( "-1,-3,-7,-9,-21,-63\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 $\"-63\"$ .\r
\n" ); document.write( "\n" ); document.write( "1*(-63) = -63
\n" ); document.write( "3*(-21) = -63
\n" ); document.write( "7*(-9) = -63
\n" ); document.write( "(-1)*(63) = -63
\n" ); document.write( "(-3)*(21) = -63
\n" ); document.write( "(-7)*(9) = -63\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 $\"2\"$ :\r
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First Number	Second Number	Sum
1	-63	1+(-63)=-62
3	-21	3+(-21)=-18
7	-9	7+(-9)=-2
-1	63	-1+63=62
-3	21	-3+21=18
-7	9	-7+9=2

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\n" ); document.write( "\n" ); document.write( "From the table, we can see that the two numbers $\"-7\"$ and $\"9\"$ add to $\"2\"$ (the middle coefficient).\r
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\n" ); document.write( "\n" ); document.write( "So the two numbers $\"-7\"$ and $\"9\"$ both multiply to $\"-63\"$ and add to $\"2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now replace the middle term $\"2x\"$ with $\"-7x%2B9x\"$ . Remember, $\"-7\"$ and $\"9\"$ add to $\"2\"$ . So this shows us that $\"-7x%2B9x=2x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"21x%5E2%2Bhighlight%28-7x%2B9x%29-3\"$ Replace the second term $\"2x\"$ with $\"-7x%2B9x\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"%2821x%5E2-7x%29%2B%289x-3%29\"$ Group the terms into two pairs.\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%283x-1%29%2B%289x-3%29\"$ Factor out the GCF $\"7x\"$ from the first group.\r
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\n" ); document.write( "\n" ); document.write( " $\"7x%283x-1%29%2B3%283x-1%29\"$ Factor out $\"3\"$ 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( " $\"%287x%2B3%29%283x-1%29\"$ Combine like terms. Or factor out the common term $\"3x-1\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"21x%5E2%2B2x-3\"$ factors to $\"%287x%2B3%29%283x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "In other words, $\"21x%5E2%2B2x-3=%287x%2B3%29%283x-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Note: you can check the answer by expanding $\"%287x%2B3%29%283x-1%29\"$ to get $\"21x%5E2%2B2x-3\"$ or by graphing the original expression and the answer (the two graphs should be identical).\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my tutoring website\r
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\n" ); document.write( "\n" ); document.write( "Jim \n" ); document.write( "

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