document.write( "Question 756643: 3. Find the complex zeros of the polynomial function. Write f in factored form.
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Algebra.Com's Answer #460345 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "F(x)=x^3-8x^2+29x-52\r\n" );
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document.write( "The possible rational zeros are ± the factors of 52,\r\n" );
document.write( "which are ±1,±2,±4,±13,±26, and ±52\r\n" );
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document.write( "You can keep trying those and the only one that gives\r\n" );
document.write( "a zero remainder and is therefore a rational zero is 4.\r\n" );
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document.write( "4|1 -8  29 -52\r\n" );
document.write( " |   4 -16  52\r\n" );
document.write( "  1 -4  13   0\r\n" );
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document.write( "So we have factored F(x) this way:\r\n" );
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document.write( "F(x) = (x-4)(x²-4x+13)\r\n" );
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document.write( "To find the other zeros we set the factor\r\n" );
document.write( "x² - 4x + 13 = 0 and use the quadratic formula:\r\n" );
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document.write( "x = \"%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29+\"\r\n" );
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document.write( "x = \"%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%2813%29+%29%29%2F%282%281%29%29+\" \r\n" );
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document.write( "x = \"%284+%2B-+sqrt%2816-52+%29%29%2F2+\"\r\n" );
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document.write( "x = \"%284+%2B-+sqrt%28-36+%29%29%2F2+\"\r\n" );
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document.write( "x = \"%284+%2B-+6i%29%2F2+\"\r\n" );
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document.write( "x = \"%282%282+%2B-+3i%29%29%2F2+\"\r\n" );
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document.write( "x = \"%28cross%282%29%282+%2B-+3i%29%29%2Fcross%282%29+\"\r\n" );
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document.write( "x = 2 ± 3i\r\n" );
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document.write( "So the other zeros are 2 + 3i and 2 - 3i\r\n" );
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document.write( "So the factored form of F(x) is\r\n" );
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document.write( "F(x) = (x - 4)[x - (2 + 3i)][x - (2 - 3i)]\r\n" );
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document.write( "or \r\n" );
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document.write( "F(x) = (x - 4)(x - 2 - 3i)(x - 2 + 3i)\r\n" );
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document.write( "Edwin
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