document.write( "Question 824421: Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.\r
\n" ); document.write( "\n" ); document.write( "f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1 \n" ); document.write( "
Algebra.Com's Answer #496448 by stanbon(75887)\"\" \"About 
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Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
\n" ); document.write( "f(x) = 3x^4 - 6x^3 + 4x^2 - 2x + 1
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\n" ); document.write( "Since the sum of the coefficients is zero, x = 1 is a root
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\n" ); document.write( "Use synthetic division to find other roots.
\n" ); document.write( "1)....3....-6....4....-2....1
\n" ); document.write( "......3....-3....1....-1..|..0\r
\n" ); document.write( "\n" ); document.write( "Again; since the sum of the coefficients is 1, x = 1 is a root
\n" ); document.write( "1)....3....-3....1....-1
\n" ); document.write( "......3....0.....1...|..0\r
\n" ); document.write( "\n" ); document.write( "Quotient: 3x^2+1 = 0
\n" ); document.write( "Factor::
\n" ); document.write( "(sqrt(3)x+i)(sqrt(3)x-i) = 0
\n" ); document.write( "----
\n" ); document.write( "Roots:: x = 1,1,sqrt(3)i/3,-sqrt(3)i/3
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\n" ); document.write( "Factor Form
\n" ); document.write( "f(x) = (x-1)^2(3x^2+1)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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