Answer: f(x) = 2x^5 - 4x^3 + x^2 - 4x + 10
Step-by-step explanation:
In order to solve this problem, we will first divide the given function f(x) by 3x+8 and then find the quotient and remainder. After that, we will write the result in the standard form.
Given: f(x) = 2x^6 - 4x + 1
Quotient: 2x^6 - 4x + 1 ÷ (3x + 8) = 2x^5 - 4x^3 + 1x^2 - 4x + 1
Remainder: R = 9
Now, we will combine the quotient and the remainder to find the function f(x).
f(x) = 2x^5 - 4x^3 + 1x^2 - 4x + 1 + 9
f(x) = 2x^5 - 4x^3 + 1x^2 - 4x + 10
Therefore, the function f(x) can be written in the standard form as:
f(x) = 2x^5 - 4x^3 + x^2 - 4x + 10