Question

question 33 (1 point) use synthetic division to evaluate the function for the indicated value of x. f(x) = 3x⁴ - 11x³ + 8x + 2, x = 2 a f(2) = -22 b f(2) = 122 c f(2) = -122 d f(2) = 22

Explanation:

Step1: Identify coefficients

The polynomial \( f(x) = 3x^4 - 11x^3 + 0x^2 + 8x + 2 \) (we add \( 0x^2 \) for the missing term). The coefficients are \( 3, -11, 0, 8, 2 \), and we use \( x = 2 \) for synthetic division.

Step2: Set up synthetic division

Write the root (2) and the coefficients:

$$
LATEXBLOCK0
$$

The last number is the remainder, which is \( f(2) \).

Answer:

a. \( f(2) = -22 \)