document.write( "Question 105799This question is from textbook college algebra
\n" ); document.write( ": what are the rational zeros and other zeros
\n" ); document.write( "What are the linear factors
\n" ); document.write( "f(x)=3x4-4x3+x2+6x-2 \n" ); document.write( "
Algebra.Com's Answer #76995 by stanbon(75887)\"\" \"About 
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what are the rational zeros and other zeros
\n" ); document.write( "What are the linear factors
\n" ); document.write( "f(x)=3x4-4x3+x2+6x-2
\n" ); document.write( "----------
\n" ); document.write( "f(-1)=0 so (x+1) is a factor
\n" ); document.write( "Using synthetic division you get:\r
\n" ); document.write( "\n" ); document.write( "-1)....3....-4....1....6....-2
\n" ); document.write( ".........3.....-7...8....-2..|..0\r
\n" ); document.write( "\n" ); document.write( "Remainder: zero
\n" ); document.write( "Quotient: 3x^3 -7x^2 + 8x -2\r
\n" ); document.write( "\n" ); document.write( "Graphing the Quotient I find a zero at x=1/3
\n" ); document.write( "1/3)....3....-7....8....-2
\n" ); document.write( "..........3.....-6...6...|..0\r
\n" ); document.write( "\n" ); document.write( "Remainder: zero
\n" ); document.write( "Quotient: 3x^2-6x+6= 3(x^2-2x+2)\r
\n" ); document.write( "\n" ); document.write( "The discriminatn for x^2-2x+2 is 4-4*1*2 is negative
\n" ); document.write( "so there are no further rational zeros or rational
\n" ); document.write( "factors.
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\n" ); document.write( "Final Answer:
\n" ); document.write( "Rational Zeroes: x= -1 and x= 1/3
\n" ); document.write( "Rational Factors: (x+1)(3x-1)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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