By applying Remainder Theorem, let us calculate and write the remainders, that I shall get when the following polynomials are divided by (x – 1).

11x³ – 12x² – x + 7

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.

Let f(x) = 11x³ – 12x² – x + 7 …(1)

When 11x³ – 12x² – x + 7 is divided by (x – 1).

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

To find zero,

x – 1 = 0

⇒ x = 1

This means that by remainder theorem, when 11x³ – 12x² – x + 7 is divided by (x – 1), the remainder comes out to be f(1).

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

Remainder = f(1)

⇒ Remainder = 11(1)³ – 12(1)² – (1) + 7

⇒ Remainder = 11 – 12 – 1 + 7

⇒ Remainder = -1 – 1 + 7

⇒ Remainder = -2 + 7

⇒ Remainder = 5

∴ the required remainder = 5