document.write( "Question 732874: What are the factors, (5 at minimum,) of 16x^9-16x? \n" ); document.write( "
Algebra.Com's Answer #448373 by Edwin McCravy(20056) $\"\"$ $\"About$
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document.write( "16x⁹ - 16x\r\n" );
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document.write( "Factor out 16x\r\n" );
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document.write( "16x(x⁸ - 16)\r\n" );
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document.write( "The parentheses contains the difference of 2 perfect squares:\r\n" );
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document.write( "16x(x⁴ - 4)(x⁴ + 4)\r\n" );
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document.write( "The parentheses contains the difference of 2 perfect squares:\r\n" );
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document.write( "16x(x² - 2)(x² + 2)(x⁴ + 4)\r\n" );
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document.write( "The 3rd parentheses can become the difference of perfect squares\r\n" );
document.write( "if we play the trick of adding and subtracting 4x²\r\n" );
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document.write( "16x(x² - 2)(x² + 2)(x⁴ + 4 + 4x² - 4x²)\r\n" );
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document.write( "Swap the 2nd and 3rd terms in the 3rd parentheses\r\n" );
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document.write( "16x(x² - 2)(x² + 2)(x⁴ + 4x² + 4 - 4x²)\r\n" );
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document.write( "Change the third parentheses to brackets and enclose its\r\n" );
document.write( "first three terms in parentheses\r\n" );
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document.write( "16x(x² - 2)(x² + 2)[(x⁴ + 4x² + 4) - 4x²]\r\n" );
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document.write( "Factor the trinomial as a perfect square\r\n" );
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document.write( "16x(x² - 2)(x² + 2)[(x² + 2)² - 4x²]\r\n" );
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document.write( "Now the bracket contains the difference of 2 perfect squares: \r\n" );
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document.write( "16x(x² - 2)(x² + 2)[(x² + 2) - 2x][(x² + 2) + 2x]\r\n" );
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document.write( "Remove the parentheses inside the brackets:\r\n" );
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document.write( "16x(x² - 2)(x² + 2)[x² + 2 - 2x][x² + 2 + 2x]\r\n" );
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document.write( "Arrange the trinmials in brackets in descending order and\r\n" );
document.write( "change the brackets to parentheses:\r\n" );
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document.write( "16x(x² - 2)(x² + 2)(x² - 2x + 2)(x² + 2x + 2)\r\n" );
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document.write( "Here are 105 factors of that, pick any 5.   \r\n" );
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document.write( "1.  1\r\n" );
document.write( "2.  2\r\n" );
document.write( "3.  4\r\n" );
document.write( "4.  8\r\n" );
document.write( "5.  16\r\n" );
document.write( "6.  x\r\n" );
document.write( "7.  (x²-2)\r\n" );
document.write( "8.  (x²+2)\r\n" );
document.write( "9.  (x²-2x+2)\r\n" );
document.write( "10.  (x²+2x+2)\r\n" );
document.write( "11.  x(x²-2)\r\n" );
document.write( "12.  x(x²+2)\r\n" );
document.write( "13.  (x²-2)(x²+2)\r\n" );
document.write( "14.  2x(x²-2)\r\n" );
document.write( "15.  x(x²+2)\r\n" );
document.write( "16.  (x²-2)(x²+2)\r\n" );
document.write( "17.  4x(x²-2)\r\n" );
document.write( "18.  x(x²+2)\r\n" );
document.write( "19.  (x²-2)(x²+2)\r\n" );
document.write( "20.  8x(x²-2)\r\n" );
document.write( "21.  x(x²+2)\r\n" );
document.write( "22.  (x²-2)(x²+2)\r\n" );
document.write( "23.  16x(x²-2)\r\n" );
document.write( "24.  x(x²+2)\r\n" );
document.write( "25.  (x²-2)(x²+2)\r\n" );
document.write( "26.  x(x²-2)(x²+2)\r\n" );
document.write( "27.  x(x²-2)(x²-2x+2)\r\n" );
document.write( "28.  x(x²-2)(x²+2x+2)\r\n" );
document.write( "29.  x(x²+2)(x²-2x+2)\r\n" );
document.write( "30.  x(x²+2)(x²+2x+2)\r\n" );
document.write( "31.  x(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "32.  (x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "33.  (x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "34.  (x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "35.  (x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "36.  2x(x²-2)(x²+2)\r\n" );
document.write( "37.  x(x²-2)(x²-2x+2)\r\n" );
document.write( "38.  x(x²-2)(x²+2x+2)\r\n" );
document.write( "39.  x(x²+2)(x²-2x+2)\r\n" );
document.write( "40.  x(x²+2)(x²+2x+2)\r\n" );
document.write( "41.  x(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "42.  (x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "43.  (x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "44.  (x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "45.  (x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "46.  4x(x²-2)(x²+2)\r\n" );
document.write( "47.  x(x²-2)(x²-2x+2)\r\n" );
document.write( "48.  x(x²-2)(x²+2x+2)\r\n" );
document.write( "49.  x(x²+2)(x²-2x+2)\r\n" );
document.write( "50.  x(x²+2)(x²+2x+2)\r\n" );
document.write( "51.  x(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "52.  (x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "53.  (x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "54.  (x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "55.  (x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "56.  8x(x²-2)(x²+2)\r\n" );
document.write( "57.  x(x²-2)(x²-2x+2)\r\n" );
document.write( "58.  x(x²-2)(x²+2x+2)\r\n" );
document.write( "59.  x(x²+2)(x²-2x+2)\r\n" );
document.write( "60.  x(x²+2)(x²+2x+2)\r\n" );
document.write( "61.  x(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "62.  (x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "63.  (x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "64.  (x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "65.  (x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "66.  16x(x²-2)(x²+2)\r\n" );
document.write( "67.  x(x²-2)(x²-2x+2)\r\n" );
document.write( "68.  x(x²-2)(x²+2x+2)\r\n" );
document.write( "69.  x(x²+2)(x²-2x+2)\r\n" );
document.write( "70.  x(x²+2)(x²+2x+2)\r\n" );
document.write( "71.  x(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "72.  (x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "73.  (x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "74.  (x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "75.  (x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "76.  x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "77.  x(x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "78.  x(x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "79.  x(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "80.  (x²-2)(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "81.  2x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "82.  x(x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "83.  x(x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "84.  x(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "85.  (x²-2)(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "86.  4x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "87.  x(x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "88.  x(x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "89.  x(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "90.  (x²-2)(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "91.  8x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "92.  x(x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "93.  x(x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "94.  x(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "95.  (x²-2)(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "96.  16x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "97.  x(x²-2)(x²+2)(x²+2x+2)\r\n" );
document.write( "98.  x(x²-2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "99.  x(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "100.  (x²-2)(x²+2)(x²-2x+2)(x²+2x+2)\r\n" );
document.write( "101.  x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "102.  2x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "103.  4x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "104.  8x(x²-2)(x²+2)(x²-2x+2)\r\n" );
document.write( "105.  16x(x²-2)(x²+2)(x²-2x+2)\r\n" );
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document.write( "Edwin
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