Answer :

Let p(x) = x^{11} + 101 and g(x) = x + 1

By using remainder theorem put value of x + 1 = 0

x + 1 = 0

x = –1

Hence, p(– 1) will give the remainder of x^{11} + 101 divided by x + 1

P(– 1) = x^{11} + 101

P(– 1) = (–1)^{11} + 101

P(– 1) = 101 – 1

P(– 1) = 100

∴ remainder is 100

Rate this question :

is divided by (x-a)

RS Aggarwal & V Aggarwal - MathematicsIn each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = 4*x*^{3}-12*x*^{2}+14*x*-3, *g*(*x*) = 2*x*-1

In each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = *x*^{3}-6*x*^{2}+2*x*-4, *g*(*x*) = 1-2*x*

In each of the following, using the remainder theorem, find the remainder when *f*(*x*) is divided by *g*(*x*):

*f*(*x*) = 2*x*^{4}-6*x*^{3}+2*x*^{2}-*x*+2, *g*(*x*) = *x*+2

When (x^{31} + 31) is divided by (x + 1), the remainder is

is divided by (3x+2)

RS Aggarwal & V Aggarwal - MathematicsFind the remainder when p (x) = 4x^{3} + 8x^{2} – 17x + 10 is divided by (2x – 1).

Show that:

(i) 𝑥 + 3 is a factor of 69 + 11𝑥−𝑥^{2} + 𝑥^{3}.

(ii) 2𝑥−3 is a factor of 𝑥 + 2𝑥^{3} – 9𝑥^{2} + 12

When p (x) = (x^{3} + ax^{2} + 2x + a) is divided by (x + a), the remainder is

If p (x) = 2x^{3} + ax^{2} + 3x – 5 and q (x) = x^{3} + x^{2} – 4x + a leave the same remainder when divided by (x – 2), show that