Question

given the function (f(x) = 8x^2 - 3x + 8). calculate the following values using synthetic division and the remainder theorem:
(f(-2) =)
(f(-1) =)
(f(0) =)
(f(1) =)
(f(2) =)

Explanation:

Step1: Apply synthetic division for \(x = -2\)

$$
LATEXBLOCK0
$$

Thus, \(f(-2) = 46\).

Step2: Apply synthetic division for \(x = -1\)

$$
LATEXBLOCK1
$$

Thus, \(f(-1) = 19\).

Step3: Apply synthetic division for \(x = 0\)

$$
LATEXBLOCK2
$$

Thus, \(f(0) = 8\).

Step4: Apply synthetic division for \(x = 1\)

$$
LATEXBLOCK3
$$

Thus, \(f(1) = 13\).

Step5: Apply synthetic division for \(x = 2\)

$$
LATEXBLOCK4
$$

Thus, \(f(2) = 34\).

Answer:

\(f(-2) = 46\)
\(f(-1) = 19\)
\(f(0) = 8\)
\(f(1) = 13\)
\(f(2) = 34\)