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 = 5

∴ the required remainder = 5.