document.write( "Question 1060705: long division: (x^3-3x^2+2x-8)/(x^2+4)\r
\n" ); document.write( "\n" ); document.write( "and find the 9th term of:
\n" ); document.write( "(x^2-2)^9\r
\n" ); document.write( "\n" ); document.write( "I need help i'm completely confused on long division and terms. I don't understand the formulas. Can you help? \n" ); document.write( "

Algebra.Com's Answer #675582 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
The second question is reliant on simply following the Binomial Theorem. You can refer to that and fill-in what you need.\r
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\n" ); document.write( "\n" ); document.write( "The long division for the polynomials works the same way as long division for regular base-ten numbers, and can be done without the condensing that you would be able if in base-ten numbers.\r
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\n" ); document.write( "\n" ); document.write( "This could be broken into steps with explanations, but here I will just show the whole thing in one finished piece:\r
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\n" ); document.write( "\n" ); document.write( "The dividend is shown toward the right, and the divisor is shown at the left, and you begin first asking, what is x^3 divided by x^2; and this is x; and so you put in the first partial quotient of x, ABOVE the x^3.
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document.write( "       |_______________________________________\r\n" );
document.write( "x^2+4  |    x^3    -3x^2    +2x      -8\r\n" );
document.write( "       |\r\n" );
document.write( "       |\r\n" );
document.write( "       |_________________\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "You need to observe that the divisor has a term, $\"0%2Ax\"$ and you should account for this term when performing the partial multiplications .
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document.write( "             x      -3\r\n" );
document.write( "       |_______________________________________\r\n" );
document.write( "x^2+4  |    x^3    -3x^2    +2x      -8\r\n" );
document.write( "       |\r\n" );
document.write( "       |    x^3    0x^2     4x\r\n" );
document.write( "       |_________________\r\n" );
document.write( "            0      -3x^2    -2x     -8\r\n" );
document.write( "                   -3x^2     0x     -12\r\n" );
document.write( "                  _______________________\r\n" );
document.write( "                    0        -2x    4\r\n" );
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document.write( "

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\n" ); document.write( "\n" ); document.write( "The quotient is $\"x-3\"$ and the remainder is $\"-2x%2B4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The entire quotient with the remainder can also be expressed according to its complete meaning, $\"x-3%2B%28-2x%2B4%29%2F%28x%5E2%2B4%29\"$ . \n" ); document.write( "

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