document.write( "Question 1176819: Graph the polynomial function that has the following properties:\r
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\n" ); document.write( "Zeros at x = -3 with multiplicity 4, x = 0 with multiplicity 1, and x = 3 with multiplicity 2\r
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\n" ); document.write( "\n" ); document.write( "Homework question from Hans Beauvoir \n" ); document.write( "
Algebra.Com's Answer #804580 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!

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\n" ); document.write( "Negative leading coefficient with an odd degree
\n" ); document.write( "Zeros at x = -3 with multiplicity 4, x = 0 with multiplicity 1, and x = 3 with multiplicity 2
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document.write( "We'll look at the zero properties first\r\n" );
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document.write( "Zero at\r\n" );
document.write( "x = -3 with multiplicity 4\r\n" );
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document.write( "That means (x+3)4 is a factor of the polynomial. 4 is even\r\n" );
document.write( "so it will \"bounce\" off the x axis at x=-3.\r\n" );
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x = 0 with multiplicity 1,
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document.write( "That means (x-0)1 or just x is a factor of the polynomial. 1 is\r\n" );
document.write( "odd so it will cut through the x axis at x=0.\r\n" );
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x = 3 with multiplicity 2
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document.write( "That means (x-3)2 is a factor of the polynomial. 2 is even\r\n" );
document.write( "so it will \"bounce\" off the x axis at x=3.\r\n" );
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document.write( "So we put those three factors together\r\n" );
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document.write( "\"%28x%2B3%29%5E4%28x%29%28x-3%29%5E2\"\r\n" );
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document.write( "The greatest power of x that will occur is x7\r\n" );
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Negative leading coefficient with an odd degree
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document.write( "That has an odd degree, 7, but not a negative leading coefficient.\r\n" );
document.write( "So we must multiply a negative sign in front:\r\n" );
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document.write( "\"-%28x%2B3%29%5E4%28x%29%28x-3%29%5E2\"\r\n" );
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document.write( "It has a negative leading coefficient so it will go down on the extreme\r\n" );
document.write( "right.  It has odd degree so it will do the opposite, go up, on the extreme\r\n" );
document.write( "left.\r\n" );
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document.write( "Multiply it out, and label the polynomial function p(x)\r\n" );
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document.write( "\"p%28x%29=-x%5E7+-+6x%5E6+%2B+9x%5E5+%2B+108x%5E4+%2B+81x%5E3+-+486x%5E2+-+729x\"\r\n" );
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document.write( "Edwin
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