What is the remainder when (x³ - 3x² - 13x + 78) is divided by (x + 4)?

Solution:

We have to find the remainder when (x³ - 3x² - 13x + 78) is divided by (x + 4)

When f(x) is divided by (x+a), then f(a) gets us the remainder according to the remainder theorem.

Using the remainder theorem, we evaluate f(-4)

f(-4) = (-4)³ -3(-4)²-13(-4)+78

= -64 -3(16) +52 +78

= -64 -48 +120

= 18

Therefore, the remainder is 18.

What is the remainder when (x³ - 3x² - 13x + 78) is divided by (x + 4)?

Summary:

The remainder when (x³ - 3x² - 13x + 78) is divided by (x + 4) is 18.