document.write( "Question 125429: Factor if possible
\n" ); document.write( "3(x-2y)^2 + 6(x-2y) - 45 \r
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\n" ); document.write( "3(x+2y+5)(x-2y-3) , 3(x-2y-5)(x-2y+3), 3(x+2y-5)(x-2y+3) , 3(x-2y+5)(x-2y-3) \n" ); document.write( "

Algebra.Com's Answer #91921 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"z=x-2y\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the expression $\"3%28x-2y%29%5E2+%2B+6%28x-2y%29+-+45+\"$ becomes $\"3z%5E2+%2B+6z+-+45\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"3z%5E2%2B6z-45\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"3%28z%5E2%2B2z-15%29\"$ Factor out the GCF $\"3\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"z%5E2%2B2z-15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"1z%5E2%2B2z-15\"$ we can see that the first term is $\"1z%5E2\"$ and the last term is $\"-15\"$ where the coefficients are 1 and -15 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient 2? Let's list all of the factors of -15:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -15:\r
\n" ); document.write( "\n" ); document.write( "1,3,5,15\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-5,-15 ...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 -15\r
\n" ); document.write( "\n" ); document.write( "(1)*(-15)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-5)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(15)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(5)\r
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\n" ); document.write( "\n" ); document.write( "note: remember, the product of a negative and a positive number is a negative number\r
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\n" ); document.write( "\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\r
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First Number	Second Number	Sum
1	-15	1+(-15)=-14
3	-5	3+(-5)=-2
-1	15	-1+15=14
-3	5	-3+5=2

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\n" ); document.write( "\n" ); document.write( "From this list we can see that -3 and 5 add up to 2 and multiply to -15\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"1z%5E2%2B2z-15\"$ , replace $\"2z\"$ with $\"-3z%2B5z\"$ (notice $\"-3z%2B5z\"$ adds up to $\"2z\"$ . So it is equivalent to $\"2z\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"1z%5E2%2Bhighlight%28-3z%2B5z%29%2B-15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"1z%5E2-3z%2B5z-15\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%281z%5E2-3z%29%2B%285z-15%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"z%28z-3%29%2B5%28z-3%29\"$ Factor out the GCF of $\"z\"$ out of the first group. Factor out the GCF of $\"5\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28z%2B5%29%28z-3%29\"$ Since we have a common term of $\"z-3\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"1z%5E2-3z%2B5z-15\"$ factors to $\"%28z%2B5%29%28z-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"1z%5E2%2B2z-15\"$ factors to $\"%28z%2B5%29%28z-3%29\"$ (since $\"1z%5E2%2B2z-15\"$ is equivalent to $\"1z%5E2-3z%2B5z-15\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"3%28z%5E2%2B2z-15%29\"$ and factors further to $\"3%28z%2B5%29%28z-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Remember we let $\"z=x-2y\"$ , so let's replace z with x-2y\r
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\n" ); document.write( "\n" ); document.write( " $\"3%28x-2y%2B5%29%28x-2y-3%29\"$ Plug in $\"z=x-2y\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"3%28x-2y%29%5E2+%2B+6%28x-2y%29+-+45+\"$ factors to $\"3%28x-2y%2B5%29%28x-2y-3%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the answer is D) \n" ); document.write( "

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