Given that f(x) = x3 + 2x2 + 3x, find the remainder when f(x + 2) isdivided by x − 2.

To find the remainder when f(x + 2) is divided by x - 2, we first need to substitute (x + 2) into the function f(x).

So, f(x + 2) = (x + 2)³ + 2(x + 2)² + 3(x + 2)

Simplify this to get: f(x + 2) = x³ + 6x² + 12x + 8 + 2x² + 8x + 8 + 3x + 6

Combine like terms to get: f(x + 2) = x³ + 8x² + 23x + 22

Now, we want to find the remainder when f(x + 2) is divided by x - 2.

We can use the Remainder Theorem, which states that the remainder when a polynomial f(x) is divided by (x - a) is equal to f(a).

So, we substitute x = 2 into f(x + 2) to find the remainder:

Remainder = f(2) = 2³ + 82² + 232 + 22 = 8 + 32 + 46 + 22 = 108

So, the remainder when f(x + 2) is divided by x - 2 is 108.