document.write( "Question 140851: Please help me solve these problems.
\n" ); document.write( "Factor. Check by multiplying
\n" ); document.write( "4x^5 y^3+16x^3 y^2+32xy and
\n" ); document.write( "9x^2=72x and
\n" ); document.write( "factor by grouping
\n" ); document.write( "21x^3-15x^2+28x-20.
\n" ); document.write( "Thank you very much! \n" ); document.write( "

Algebra.Com's Answer #102493 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 1\r
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\n" ); document.write( "\n" ); document.write( " $\"4x%5E5y%5E3%2B16x%5E3y%5E2%2B32xy\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"4xy%28x%5E4y%5E2%2B4x%5E2y%2B8%29\"$ Factor out the GCF $\"4xy\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now let's focus on the inner expression $\"x%5E4y%5E2%2B4x%5E2y%2B8\"$ \r
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\n" ); document.write( "\n" ); document.write( "Looking at $\"1x%5E4y%5E2%2B4x%5E2y%2B8\"$ we can see that the first term is $\"1x%5E4y%5E2\"$ and the last term is $\"8\"$ where the coefficients are 1 and 8 respectively.\r
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\n" ); document.write( "\n" ); document.write( "Now multiply the first coefficient 1 and the last coefficient 8 to get 8. Now what two numbers multiply to 8 and add to the middle coefficient 4? Let's list all of the factors of 8:\r
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\n" ); document.write( "\n" ); document.write( "Factors of 8:\r
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\n" ); document.write( "\n" ); document.write( "-1,-2,-4,-8 ...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 8\r
\n" ); document.write( "\n" ); document.write( "1*8\r
\n" ); document.write( "\n" ); document.write( "2*4\r
\n" ); document.write( "\n" ); document.write( "(-1)*(-8)\r
\n" ); document.write( "\n" ); document.write( "(-2)*(-4)\r
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\n" ); document.write( "\n" ); document.write( "note: remember two negative numbers multiplied together make a positive number\r
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\n" ); document.write( "\n" ); document.write( "Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4\r
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First Number	Second Number	Sum
1	8	1+8=9
2	4	2+4=6
-1	-8	-1+(-8)=-9
-2	-4	-2+(-4)=-6

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\n" ); document.write( "\n" ); document.write( "None of these pairs of factors add to 4. So the expression $\"1x%5E4y%5E2%2B4x%5E2y%2B8\"$ cannot be factored\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "\n" ); document.write( "So $\"4x%5E5y%5E3%2B16x%5E3y%5E2%2B32xy\"$ factors to $\"4xy%28x%5E4y%5E2%2B4x%5E2y%2B8%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%5E2=72x\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"9x%5E2-72x=0\"$ Subtract 72x from both sides. \r
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\n" ); document.write( "\n" ); document.write( " $\"9x%28x-8%29=0\"$ Factor out the GCF 9x\r
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\n" ); document.write( "\n" ); document.write( "Now set each factor equal to zero:\r
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\n" ); document.write( "\n" ); document.write( " $\"9x=0\"$ or $\"x-8=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"x=0\"$ or $\"x=8\"$ Now solve for x in each case\r
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\n" ); document.write( "\n" ); document.write( "So our answers are
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\n" ); document.write( "\n" ); document.write( " $\"x=0\"$ or $\"x=8\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 3\r
\n" ); document.write( "\n" ); document.write( " $\"21x%5E3-15x%5E2%2B28x-20\"$ Start with the given expression\r
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\n" ); document.write( "\n" ); document.write( " $\"%2821x%5E3-15x%5E2%29%2B%2828x-20%29\"$ Group like terms\r
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\n" ); document.write( "\n" ); document.write( " $\"3x%5E2%287x-5%29%2B4%287x-5%29\"$ Factor out the GCF $\"3x%5E2\"$ out of the first group. Factor out the GCF $\"4\"$ out of the second group\r
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\n" ); document.write( "\n" ); document.write( " $\"%283x%5E2%2B4%29%287x-5%29\"$ Since we have the common term $\"7x-5\"$ , we can combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So $\"21x%5E3-15x%5E2%2B28x-20\"$ factors to $\"%283x%5E2%2B4%29%287x-5%29\"$
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