document.write( "Question 78330: Please help me solve this:\r
\n" ); document.write( "\n" ); document.write( "\"%282x%5E2-2%29%2F%286x%2B6%29\" times \"%286x%5E2%2B18x%29%2F%28x%5E2%2B2x-3%29\"
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Algebra.Com's Answer #56164 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"%28%282x%5E2-2%29%2F%286x%2B6%29%29%2A%28%286x%5E2%2B18x%29%2F%28x%5E2%2B2x-3%29%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%28%282x%5E2-2%29%2F%286%28x%2B1%29%29%29%2A%28%286x%5E2%2B18x%29%2F%28x%5E2%2B2x-3%29%29\" Factor a 6 out of \"6x%2B6\"\r
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\n" ); document.write( "\n" ); document.write( "\"%282%28x%5E2-1%29%2F%286%28x%2B1%29%29%29%2A%28%286x%5E2%2B18x%29%2F%28x%5E2%2B2x-3%29%29\" Factor a 2 out of \"2x%5E2-2\"\r
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\n" ); document.write( "\n" ); document.write( "\"%282%28x%5E2-1%29%2F%286%28x%2B1%29%29%29%2A%286x%28x%2B3%29%2F%28x%5E2%2B2x-3%29%29\" Factor a 6x out of \"6x%5E2%2B18x\"\r
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\n" ); document.write( "\n" ); document.write( "Now factor \"x%5E2-1\"\r
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Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B0%2Ax%2B-1\", first we need to ask ourselves: What two numbers multiply to -1 and add to 0? Lets find out by listing all of the possible factors of -1
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1,
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\n" ); document.write( " -1,List the negative factors as well. This will allow us to find all possible combinations
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\n" ); document.write( " These factors pair up to multiply to -1.
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\n" ); document.write( " (-1)*(1)=-1
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\n" ); document.write( " Now which of these pairs add to 0? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 0
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First Number|Second Number|Sum
1|-1|1+(-1)=0
-1|1|(-1)+1=0
We can see from the table that -1 and 1 add to 0.So the two numbers that multiply to -1 and add to 0 are: -1 and 1\r\n" ); document.write( " \r\n" ); document.write( " Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" ); document.write( " \r\n" ); document.write( " \"%28x%2Ba%29%28x%2Bb%29\"substitute a=-1 and b=1\r\n" ); document.write( " \r\n" ); document.write( " So the equation becomes:\r\n" ); document.write( " \r\n" ); document.write( " (x-1)(x+1)\r\n" ); document.write( " \r\n" ); document.write( " Notice that if we foil (x-1)(x+1) we get the quadratic \"1%2Ax%5E2%2B0%2Ax%2B-1\" again\n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "Now factor \"x%5E2%2B2x-3\"\r
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Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor \"1%2Ax%5E2%2B2%2Ax%2B-3\", first we need to ask ourselves: What two numbers multiply to -3 and add to 2? Lets find out by listing all of the possible factors of -3
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\n" ); document.write( " Factors:
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\n" ); document.write( " 1,3,
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\n" ); document.write( " -1,-3,List the negative factors as well. This will allow us to find all possible combinations
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\n" ); document.write( " These factors pair up to multiply to -3.
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\n" ); document.write( " (-1)*(3)=-3
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\n" ); document.write( " Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
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First Number|Second Number|Sum
1|-3|1+(-3)=-2
-1|3|(-1)+3=2
We can see from the table that -1 and 3 add to 2.So the two numbers that multiply to -3 and add to 2 are: -1 and 3\r\n" ); document.write( " \r\n" ); document.write( " Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:\r\n" ); document.write( " \r\n" ); document.write( " \"%28x%2Ba%29%28x%2Bb%29\"substitute a=-1 and b=3\r\n" ); document.write( " \r\n" ); document.write( " So the equation becomes:\r\n" ); document.write( " \r\n" ); document.write( " (x-1)(x+3)\r\n" ); document.write( " \r\n" ); document.write( " Notice that if we foil (x-1)(x+3) we get the quadratic \"1%2Ax%5E2%2B2%2Ax%2B-3\" again\n" ); document.write( "

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\n" ); document.write( "\n" ); document.write( "So after all of that we get \r
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\n" ); document.write( "\n" ); document.write( " Notice these terms cancel\r
\n" ); document.write( "\n" ); document.write( "So we're left with\r
\n" ); document.write( "\n" ); document.write( "\"%282%2F6%29%2A%286x%2F1%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"%282%2A6x%2F6%29\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"%2812x%2F6%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"2x\" Divide \r
\n" ); document.write( "\n" ); document.write( "So the expression \"%28%282x%5E2-2%29%2F%286x%2B6%29%29%2A%28%286x%5E2%2B18x%29%2F%28x%5E2%2B2x-3%29%29\" reduces to \r
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