To find the third zero of the polynomial 3x^3 - 2x^2 - 7x - 2, we can use the fact that the sum of the zeros of a polynomial is equal to the opposite of the coefficient of the second term divided by the coefficient of the leading term.

Sum of zeros formula:
The sum of the zeros of a polynomial P(x) = ax^3 + bx^2 + cx + d is given by the formula:
Sum of zeros = -b/a

In this case, the coefficient of the second term (b) is -2 and the coefficient of the leading term (a) is 3. Therefore, the sum of the zeros is:
Sum of zeros = -(-2) / 3 = 2/3

Using the known zeros:
We know that 2 and -1/3 are two of the zeros of the polynomial. Let's denote the third zero as k.

Since the sum of the zeros is 2/3, we can write the equation:
2 + (-1/3) + k = 2/3

Simplifying the equation, we get:
k = 2/3 - 2 + 1/3
k = (2 + 1 - 6) / 3
k = -3/3
k = -1

Therefore, the third zero of the polynomial is -1.

Summary:
The polynomial 3x^3 - 2x^2 - 7x - 2 has three zeros: 2, -1/3, and -1. We found the third zero by using the fact that the sum of the zeros is equal to -b/a, where b is the coefficient of the second term and a is the coefficient of the leading term. Then, we used the known zeros to set up an equation and solve for the third zero.

by dividing them u can find the third zero..