document.write( "Question 524522: how do you find a polynomial of degree 4 with -2 as a zero of multiplicity 2 and 0 and 3 as zeros of multiplicity 1 \n" ); document.write( "
Algebra.Com's Answer #347776 by Edwin McCravy(20059)\"\" \"About 
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how do you find a polynomial of degree 4 with -2 as a zero
\n" ); document.write( "of multiplicity 2 and 0 and 3 as zeros of multiplicity 1.
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document.write( "Make a row of equations with x = each of the zeros, \r\n" );
document.write( "as many times as their multiplicities:\r\n" );
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document.write( "      x = -2,       x = -2,    x = 0,        x = 3\r\n" );
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document.write( "Get 0 on the right of each equation:\r\n" );
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document.write( "  x + 2 = 0     x + 2 = 0      x = 0,    x - 3 = 0  \r\n" );
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document.write( "Write the product of all the left sides:\r\n" );
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document.write( "         (x + 2)(x + 2)(x)(x - 3) = 0\r\n" );
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document.write( "Multiply them all together:\r\n" );
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document.write( "           (x2 + 4x + 4)(x2 - 3x) = 0\r\n" );
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document.write( "x4 - 3x3 + 4x3 - 12x2 + 4x2 - 12x = 0 \r\n" );
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document.write( "Collect like terms\r\n" );
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document.write( "              x4 + x3 - 8x2 - 12x = 0 \r\n" );
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document.write( "Set P(x) = the left side:\r\n" );
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document.write( "          P(x) = x4 + x3 - 8x2 - 12x\r\n" );
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document.write( "Edwin
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