What is the remainder when (x³ - 4x² - 12x + 9) is divided by (x + 2)?

Solution:

Given, f(x) = x³ - 4x² - 12x + 9

This problem can be solved by using the remainder theorem.

The above function divided by (x + 2) implies that (x + 2) is a factor of the function.

x + 2 = 0

⇒ x = -2

f(-2) = (-2)³ - 4(-2)² -12(-2) + 9

By further calculation

f(-2) = (-8) - 4 (4) + 24 + 9

So we get

f(-2) = -8 - 16 + 24 + 9

f(-2) = 9

Therefore, the remainder is 9.

What is the remainder when (x³ - 4x² - 12x + 9) is divided by (x + 2)?

Summary:

The remainder when (x³ - 4x² - 12x + 9) is divided by (x + 2) is 9.