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).

x3 – 3x2 + 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) = x3 – 3x2 + 4x + 50 …(1)


When x3 – 3x2 + 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 x3 – 3x2 + 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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