document.write( "Question 54472This question is from textbook ALGEBRA AND TRIGONOMETRY
\n" ); document.write( ": PLEASE HELP ME WITH THIS PROBLEM:
\n" ); document.write( "Find the polynominal f(X) of degree three that has zeroes at 1, 2, and 4 such that f(0)=-16. \n" ); document.write( "

Algebra.Com's Answer #36720 by Edwin McCravy(20055) $\"\"$ $\"About$

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PLEASE HELP ME WITH THIS PROBLEM:\r\n" );
document.write( "Find the polynominal f(X) of degree three \r\n" );
document.write( "that has zeroes at 1, 2, and 4 such that\r\n" );
document.write( "f(0) = -16.\r\n" );
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document.write( "To have zero 1 it must have factor (x - 1)\r\n" );
document.write( "To have zero 2 it must have factor (x - 2)\r\n" );
document.write( "To have zero 4 it must have factor (x - 4)\r\n" );
document.write( "It may have any non-zero constant factor, \r\n" );
document.write( "say k\r\n" );
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document.write( "Then \r\n" );
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document.write( "f(x) = k(x - 1)(x - 2)(x - 4)\r\n" );
document.write( "f(0) = k(0 - 1)(0 - 2)(0 - 4)\r\n" );
document.write( "f(0) = k(-1)(-2)(-4)\r\n" );
document.write( "f(0) = -8k\r\n" );
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document.write( "Since we are given f(0) = -16\r\n" );
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document.write( "-16 = -8k\r\n" );
document.write( "  2 = k\r\n" );
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document.write( "So\r\n" );
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document.write( "f(x) = k(x - 1)(x - 2)(x - 4)\r\n" );
document.write( "f(x) = 2(x - 1)(x - 2)(x - 4)\r\n" );
document.write( "f(x) = 2(x - 1)(x² - 6x + 8)\r\n" );
document.write( "f(x) = 2(x³ - 6x² + 8x - x² + 6x - 8)\r\n" );
document.write( "f(x) = 2(x³ - 7x² + 14x - 8)\r\n" );
document.write( "f(x) = 2x³ - 14x² + 28x - 16\r\n" );
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document.write( "Edwin McCravy

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