document.write( "Question 55882: (x^3-8)/(x^2+2x+4) please help simplify \n" ); document.write( "
Algebra.Com's Answer #37887 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
(x^3-8)/(x^2+2x+4) please help simplify\r\n" );
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document.write( "This problem can be done either of two ways.\r\n" );
document.write( "You are probably supposed to do it by factoring.\r\n" );
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document.write( "     x³ - 8\r\n" );
document.write( " -------------\r\n" );
document.write( "  x² + 2x + 4 \r\n" );
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document.write( "You MUST memorize the methods of factoring\r\n" );
document.write( "the sum or difference of two cubes if you\r\n" );
document.write( "haven't memorized them already. They are:\r\n" );
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document.write( "A³ + B³ factors as (A + B)(A² - AB + B²)\r\n" );
document.write( "A³ - B³ factors as (A - B)(A² + AB + B²)\r\n" );
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document.write( "Yes, you MUST memorize them!\r\n" );
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document.write( "The numerator of the fraction is x³ - 8,\r\n" );
document.write( "which can be written x³ - 2³, so it can\r\n" );
document.write( "be factored as (x - 2)(x² + 2x + 4)\r\n" );
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document.write( "  (x - 2)(x² + 2x + 4)\r\n" );
document.write( " ----------------------\r\n" );
document.write( "       x² + 2x + 4\r\n" );
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document.write( "OR\r\n" );
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document.write( "  (x - 2)(x² + 2x + 4)\r\n" );
document.write( " ----------------------\r\n" );
document.write( "      (x² + 2x + 4)\r\n" );
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document.write( "Now you can cancel the (x² + 2x + 4)'s\r\n" );
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document.write( "             1\r\n" );
document.write( "  (x - 2)(x² + 2x + 4)\r\n" );
document.write( " ----------------------\r\n" );
document.write( "      (x² + 2x + 4)\r\n" );
document.write( "          1\r\n" );
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document.write( "and all that's left is\r\n" );
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document.write( "    (x - 2)\r\n" );
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document.write( "or\r\n" );
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document.write( "     x - 2\r\n" );
document.write( " \r\n" );
document.write( "=====================\r\n" );
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document.write( "The other way to do that problem is by long division.\r\n" );
document.write( "But your teacher probably wanted you to do it by\r\n" );
document.write( "factoring instead. But here is how it could have\r\n" );
document.write( "been done by long division:\r\n" );
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document.write( "     x³ - 8\r\n" );
document.write( " -------------\r\n" );
document.write( "  x² + 2x + 4\r\n" );
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document.write( "                        x - 2\r\n" );
document.write( "x² + 2x + 4)x³ + 0x² + 0x - 8\r\n" );
document.write( "            x³ + 2x² + 4x\r\n" );
document.write( "                -2x² - 4x - 8\r\n" );
document.write( "                -2x² - 4x - 8\r\n" );
document.write( "                            0   \r\n" );
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document.write( "Edwin
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