document.write( "Question 145714: 36x4-8x3-28x2= \n" ); document.write( "

Algebra.Com's Answer #106337 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm assuming you want to factor right?\r
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\n" ); document.write( "\n" ); document.write( " $\"36x%5E4-8x%5E3-28x%5E2\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E2%289x%5E2-2x-7%29\"$ Factor out the GCF $\"4x%5E2\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"9x%5E2-2x-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"9x%5E2-2x-7\"$ we can see that the first term is $\"9x%5E2\"$ and the last term is $\"-7\"$ where the coefficients are 9 and -7 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 9 and the last coefficient -7 to get -63. Now what two numbers multiply to -63 and add to the middle coefficient -2? Let's list all of the factors of -63:\r
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\n" ); document.write( "\n" ); document.write( "Factors of -63:\r
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\n" ); document.write( "\n" ); document.write( "-1,-3,-7,-9,-21,-63 ...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 -63\r
\n" ); document.write( "\n" ); document.write( "(1)*(-63)\r
\n" ); document.write( "\n" ); document.write( "(3)*(-21)\r
\n" ); document.write( "\n" ); document.write( "(7)*(-9)\r
\n" ); document.write( "\n" ); document.write( "(-1)*(63)\r
\n" ); document.write( "\n" ); document.write( "(-3)*(21)\r
\n" ); document.write( "\n" ); document.write( "(-7)*(9)\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	-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 this list we can see that 7 and -9 add up to -2 and multiply to -63\r
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\n" ); document.write( "\n" ); document.write( "Now looking at the expression $\"9x%5E2-2x-7\"$ , replace $\"-2x\"$ with $\"7x%2B-9x\"$ (notice $\"7x%2B-9x\"$ adds up to $\"-2x\"$ . So it is equivalent to $\"-2x\"$ )\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%5E2%2Bhighlight%287x%2B-9x%29%2B-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's factor $\"9x%5E2%2B7x-9x-7\"$ by grouping:\r
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\n" ); document.write( "\n" ); document.write( " $\"%289x%5E2%2B7x%29%2B%28-9x-7%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"x%289x%2B7%29-1%289x%2B7%29\"$ Factor out the GCF of $\"x\"$ out of the first group. Factor out the GCF of $\"-1\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%28x-1%29%289x%2B7%29\"$ Since we have a common term of $\"9x%2B7\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"9x%5E2%2B7x-9x-7\"$ factors to $\"%28x-1%29%289x%2B7%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "So this also means that $\"9x%5E2-2x-7\"$ factors to $\"%28x-1%29%289x%2B7%29\"$ (since $\"9x%5E2-2x-7\"$ is equivalent to $\"9x%5E2%2B7x-9x-7\"$ )\r
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\n" ); document.write( "\n" ); document.write( "So our expression goes from $\"4x%5E2%289x%5E2-2x-7%29\"$ and factors further to $\"4x%5E2%28x-1%29%289x%2B7%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So $\"36x%5E4-8x%5E3-28x%5E2\"$ factors to $\"4x%5E2%28x-1%29%289x%2B7%29\"$ \r
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