Answer :

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) = x^{3} – 3x^{2} + 4x + 50 …(1)

When x^{3} – 3x^{2} + 4x + 50 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 x^{3} – 3x^{2} + 4x + 50 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 = (1)^{3} – 3(1)^{2} + 4(1) + 50

⇒ Remainder = 1 – 3 + 4 + 50

⇒ Remainder = 1 + 1 + 50

⇒ Remainder = 52

∴ the required remainder = 52

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