Q. 2 B5.0( 4 Votes )

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

x^{3} – 3x^{2} + 4x + 50

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

Rate this question :

By applying Remainder Theorem, let us calculate and write the remainder that I shall get in every cases, when x^{3} – 3x^{2} + 2x + 5 is divided by

x – 2

West Bengal MathematicsBy applying Remainder Theorem, let us calculate and write the remainder that I shall get in every cases, when x^{3} – 3x^{2} + 2x + 5 is divided by

2x + 1

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

11x^{3} – 12x^{2} – x + 7

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

4x^{3} + 4x^{2} – x – 1

Applying Remainder Theorem, let us calculate whether the polynomial.

P(x) = 4x^{3} + 4x^{2} – x – 1 is a multiple of (2x + 1) or not.

Applying Remainder Theorem, let us write the remainders, when,

the polynomial x^{3} – ax^{2} + 2x – a is divided by (x – a)

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

x^{3} – 6x^{2} + 13x + 60

Let us show that if n be any positive integer (even or odd), the x – y never be a factor of the polynomial x^{n} + y^{n}.