Find the remainder when f(x) = 4x³ - 20x - 50 is divided by x - 3.

Solution:

Here we use remainder theorem to determine the value.

The remainder theorem is stated as follows:

When a polynomial a(x) is divided by a linear polynomial b(x) whose zero is x = k, the remainder is given by r = a(k). 

Given, f(x) = 4x³ - 20x - 50

The above function divided by (x - 3) implies that (x - 3) is a factor of the function.

So, x = 3

By substituting it in the equation

f(3) = 4(3)³ - 20(3) - 50

By further calculation

f(3) = 108 - 60 - 50

So we get,

f(3) = -2

Therefore, the remainder is -2.

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Find the remainder when f(x) = 4x³ - 20x - 50 is divided by x - 3.

Summary:

The remainder when f(x) = 4x³ - 20x - 50 is divided by (x - 3) is -2.