document.write( "Question 1050510: Find all real and complex zeros of the polynomial, and write p(x) as the product of linear factors.
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Algebra.Com's Answer #666097 by ikleyn(52777)\"\" \"About 
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\n" ); document.write( "Find all real and complex zeros of the polynomial, and write p(x) as the product of linear factors.
\n" ); document.write( "P(x)=x^4-9x^2+4x+12
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document.write( "Apply grouping to factor P(x):\r\n" );
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document.write( "\"x%5E4-9x%5E2%2B4x%2B12\" = \"%28x%5E4-9x%5E2%29%2B%284x%2B12%29\" = \"x%5E2%28x%5E2-9%29+%2B+4%2A%28x%2B3%29\" = \"x%5E2%2A%28x%2B3%29%2A%28x-3%29+%2B+4%2A%28x%2B3%29\" = \"%28x%2B3%29%2A%28x%5E2%2A%28x-3%29%2B4%29\" = \"%28x%2B3%29%2A%28x%5E3-3x%5E2%2B4%29\". \r\n" );
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document.write( "So, one root is x = -3.\r\n" );
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document.write( "Next, transform and factor the polynomial Q(x) = x^3 - 3x^2 + 4.\r\n" );
document.write( "Add and distract x^2 and then apply grouping, again:\r\n" );
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document.write( "\"x%5E3+-+3x%5E2+%2B+4\" = \"%28x%5E3+%2B+x%5E2%29+-+%284x%5E2+-4%29\" = \"x%5E2%2A%28x%2B1%29+-+4%2A%28x%5E2-1%29\" = \"x%5E2%2A%28x%2B1%29+-+4%2A%28x%2B1%29%2A%28x-1%29\" = \"%28x%2B1%29%2A%28x%5E2-4%29\" = \"%28x%2B1%29%2A%28x%2B2%29%2A%28x-2%29\".\r\n" );
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document.write( "The roots of the polynomial Q(x) are -1, -2, 2.\r\n" );
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document.write( "Answer. The roots of the polynomial P(x) are -3, -2, -1, and 2.\r\n" );
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