SOLUTION: For the function f(x) = 3x^4- 4x^3 +x^2+ 6x-2 a. State the degree of the polynomial. b. State the number of zeros the polynomial function will have. c. Use the Rational Zero T

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Question 1126680: For the function f(x) = 3x^4- 4x^3 +x^2+ 6x-2
a. State the degree of the polynomial.
b. State the number of zeros the polynomial function will have.
c. Use the Rational Zero Theorem to list all of the possible rational zeros
d. Use your calculator to determine which numbers in the list of rational zeros are probable rational
zeros.
e. Use synthetic division to verify one rational zero.
f. Use synthetic division or other algebraic methods to find all remaining zeros. List all of the zeros
of the polynomial function.
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Possible zeros may be -1, 1, -1/3, 1/3, -2/3, 2/3, -2, 2.

Expect up to four zeros, because degree is four.

Try synthetic division and you will find zeros of -1, and 1/3.
Factor still to check is
which using solution for quadratic equation shows zeros of 1-i and 1+i.