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.

When x^{3} – 3x^{2} + 2x + 5 is divided by (x + 2).

Let f(x) = x^{3} – 3x^{2} + 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 x^{3} – 3x^{2} + 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

Rate this question :

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

If the polynomialWest Bengal Mathematics

Let us show that West Bengal Mathematics

Let us show that West Bengal Mathematics

Let us show that West Bengal Mathematics

If the polynomialWest Bengal Mathematics