What is the remainder when (x³ - 7x² - 18x + 42) is divided by (x + 3)?

Solution:

Using remainder theorem, we can find the remainder.

Given,

f(x) = x³ - 7x² - 18x + 42

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

So, x = -3

f(-3) = (-3)³ - 7(-3)² -18(-3) + 42

By further simplification

f(-3) = (-27) - 7 (9) + 54 + 42

So we get

f(-3) = -27 - 63 + 54 + 42

f(-3) = 6

Therefore, the remainder is 6.

What is the remainder when (x³ - 7x² - 18x + 42) is divided by (x + 3)?

Summary:

The remainder when (x³ - 7x² - 18x + 42) is divided by (x + 3) is 6. We have used remainder theorem to determine the required value.