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

2x + 1

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 (2x + 1).

Let f(x) = x³ – 3x² + 2x + 5 …(1)

Now, let’s find out the zero of the linear polynomial, (2x + 1).

To find zero,

2x + 1 = 0

⇒ 2x = -1

⇒ x = -1/2

This means that by remainder theorem, when x³ – 3x² + 2x + 5 is divided by (2x + 1), the remainder comes out to be f(-1/2).

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

Remainder = f(-1/2)

⇒ Remainder

⇒ Remainder

⇒ Remainder

⇒ Remainder

⇒ Remainder

⇒ Remainder

∴ the required remainder = 25/8