Final answer:
To find the rational zeros of the polynomial 2x³ - 9x² - 6x, use the Rational Root Theorem to determine the possible zeros and then test them using long division or synthetic division.
Step-by-step explanation:
The given polynomial is 2x³ - 9x² - 6x. To find the rational zeros, we can use the Rational Root Theorem. According to the theorem, the possible rational zeros of the polynomial will be the factors of the constant term, 6, divided by the factors of the leading coefficient, 2.
The factors of 6 are 1, 2, 3, and 6. The factors of 2 are 1 and 2. So, the possible rational zeros are:
- x = 1
- x = 2
- x = 3
- x = 6
- x = -1
- x = -2
- x = -3
- x = -6
To determine which of these zeros are actual zeros of the polynomial, we can either use long division or synthetic division.