Q. 1 B5.0( 6 Votes )

By applying Remai

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 x3 – 3x2 + 2x + 5 is divided by (x + 2).


Let f(x) = x3 – 3x2 + 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 x3 – 3x2 + 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


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