I don't understand this.

The question is use the remainder theorem to evaluate P(x) as given.

1. P(x)=3x^3+11x^2+2x-16
and it gives me P(1/3)

To use the remainder theorem to evaluate P(x) at a specific value, you need to understand what the remainder theorem is and how to apply it.

The remainder theorem states that if you divide a polynomial P(x) by (x - a), where "a" is a constant, then the remainder of that division will be equal to P(a). In other words, if you substitute the value "a" into P(x) and calculate the result, you will get the same value as the remainder when you divide P(x) by (x - a).

In your case, you are given the polynomial P(x) = 3x^3 + 11x^2 + 2x - 16 and asked to find P(1/3). To evaluate P(1/3) using the remainder theorem, you need to divide P(x) by (x - 1/3) and calculate the remainder.

To divide P(x) by (x - 1/3), you can use long division or synthetic division. Since the degree of P(x) is 3, long division is more suitable in this case.

Here's how you can do long division to find the remainder:

3x^2 + 12x + 38
_____________________
x - 1/3 | 3x^3 + 11x^2 + 2x - 16
(3x^3 - x^2)
_____________
12x^2 + 2x
(12x^2 - 4x)
__________
6x - 16
(6x - 2)
_______
-14

After performing the long division, you find that the remainder is -14. Therefore, P(1/3) = -14.