What are all the possible rational zeros for #y=30x^3-x^2-6x+1# and how do you find all zeros?
Use the Rational Zero Theorem, synthetic division, and factoring.
According to the Rational Zero Theorem, the list of all possible rational zeros is obtained by dividing all the factors of the constant term 1 by all the factors of the leading coefficient term 30.
The possible factors of 1 are
The possible factors of 30 are
The possible zeros are:
To find all the zeros, use synthetic division. Pick one of the possible zeros as a divisor. If the remainder is zero, the divisor is a zero. If the remainder is not zero, choose another possible zero and try again. I chose 1/3 because I "cheated" and first checked the zeros using a graphing utility.
Write the quotient using the coefficients found in synthetic division and set it equal to zero.
Factor and solve to find the remaining zeros:
The three zeros are