document.write( "Question 702628: factor the sum of cubes\r
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Algebra.Com's Answer #433079 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Factor: \r\n" );
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document.write( "1 + x³\r\n" );
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document.write( "There are two ways to do it.\r\n" );
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document.write( "First method: Long division:\r\n" );
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document.write( "Write it in descending powers and put in placeholders \r\n" );
document.write( "for the x² and x terms:\r\n" );
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document.write( "x³ + 0x² + 0x + 1\r\n" );
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document.write( "This can be divided evenly by x + 1\r\n" );
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document.write( "            x² -  x + 1\r\n" );
document.write( "x + 1)x³ + 0x² + 0x + 1\r\n" );
document.write( "      x³ +  x²\r\n" );
document.write( "           -x² + 0x\r\n" );
document.write( "           -x² -  x\r\n" );
document.write( "                  x + 1\r\n" );
document.write( "                  x + 1\r\n" );
document.write( "                      0 \r\n" );
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document.write( "So you see that it factors as divisor times quotient:\r\n" );
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document.write( "    (x + 1)(x² - x + 1) \r\n" );
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document.write( "Second method:\r\n" );
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document.write( "But most people just learn the rule for factoring\r\n" );
document.write( "sum and difference of cubes, so they won't have\r\n" );
document.write( "to do the long division like I did above.\r\n" );
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document.write( "The sign between the cube terms is the same sign\r\n" );
document.write( "as the sign in the first factor and opposite\r\n" );
document.write( "the sign in the second factor.\r\n" );
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document.write( "A³ ± B³ = (A ± B)(A² ∓ AB + B²)\r\n" );
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document.write( "1³ + x³ = (1 + x)(1² - 1x + x²)\r\n" );
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document.write( "        = (1 + x)(1 - x + x²)\r\n" );
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document.write( "That's the same as (x + 1)(x² - x + 1).\r\n" );
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document.write( "Edwin
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