By applying Remainder Theorem, let us calculate and write the remainder that I shall get in every cases, when x³ – 3x² + 2x + 5 is divided by

x + 2

Remainder theorem says that,

f(x) is a polynomial of degree n (n ≥ 1) and ‘a’ is any real number. If f(x) is divided by (x – a), then the remainder will be f(a).

Let us solve the following questions on the basis of this remainder theorem.

When x³ – 3x² + 2x + 5 is divided by (x + 2).

Let f(x) = x³ – 3x² + 2x + 5 …(1)

Now, let’s find out the zero of the linear polynomial, (x + 2).

To find zero,

x + 2 = 0

⇒ x = -2

This means that by remainder theorem, when x³ – 3x² + 2x + 5 is divided by (x + 2), the remainder comes out to be f(-2).

From equation (1), remainder can be calculated as,

Remainder = f(-2)

⇒ Remainder = (-2)³ – 3(-2)² + 2(-2) + 5

⇒ Remainder = -8 – 12 – 4 + 5

⇒ Remainder = -19

∴ the required remainder = -19