SOLUTION: what are the rational zeros and other zeros What are the linear factors f(x)=3x4-4x3+x2+6x-2

Question 105799This question is from textbook college algebra
: what are the rational zeros and other zeros
What are the linear factors
f(x)=3x4-4x3+x2+6x-2 This question is from textbook college algebra

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
what are the rational zeros and other zeros
What are the linear factors
f(x)=3x4-4x3+x2+6x-2
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f(-1)=0 so (x+1) is a factor
Using synthetic division you get:
-1)....3....-4....1....6....-2
.........3.....-7...8....-2..|..0
Remainder: zero
Quotient: 3x^3 -7x^2 + 8x -2
Graphing the Quotient I find a zero at x=1/3
1/3)....3....-7....8....-2
..........3.....-6...6...|..0
Remainder: zero
Quotient: 3x^2-6x+6= 3(x^2-2x+2)
The discriminatn for x^2-2x+2 is 4-4*1*2 is negative
so there are no further rational zeros or rational
factors.
-------------
Final Answer:
Rational Zeroes: x= -1 and x= 1/3
Rational Factors: (x+1)(3x-1)
===================
Cheers,
Stan H.

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