# What are all the possible rational zeros for #y=30x^3-x^2-6x+1# and how do you find all zeros?

##### 1 Answer

#### Answer:

Use the Rational Zero Theorem, synthetic division, and factoring.

#### Explanation:

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.

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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