document.write( "Question 690480: f(x)=x^6-x^5-x^4+x^3\r
\n" ); document.write( "\n" ); document.write( "find all the zeros and the multiplicity of each zero. \r
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Algebra.Com's Answer #426313 by nerdybill(7384)\"\" \"About 
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f(x)=x^6-x^5-x^4+x^3
\n" ); document.write( "find all the zeros and the multiplicity of each zero.
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\n" ); document.write( "x^6-x^5-x^4+x^3
\n" ); document.write( "x^3(x^3-x^2-x+1)
\n" ); document.write( "now, we find roots of polynomial within parentheses...try a 1 first using synthetic division:
\n" ); document.write( "1 1 -1 -1 1
\n" ); document.write( " 1 0 -1
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\n" ); document.write( " 1 0 -1 0
\n" ); document.write( "now, we have
\n" ); document.write( "x^3(x-1)(x^2-1)
\n" ); document.write( "difference of squares:
\n" ); document.write( "x^3(x-1)(x-1)(x+1)
\n" ); document.write( "x^3(x-1)^2(x+1)
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\n" ); document.write( "Zeros are:
\n" ); document.write( "x=0 with multiplicity of 3
\n" ); document.write( "x=1 with multiplicity of 2
\n" ); document.write( "x=-1 with multiplicity of 1\r
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