If `x^(51)+ 51` is divided by `x + 1 ` , then the remainder is

Polynomial P(x) is divided by (x-3) , the remainder if 6.If P(x) is divided by (x^2-9) , then the remainder is g(x) . Then the value of g(2) is ___________.

The value of a when x^(2) + 2x + a is divided by (x - 1), the remainder is 1, is

If f(x)=x^3-3x^2+2x+a is divisible by x-1, then find the remainder when f(x) is divided by x-2.

If 8x^(3) - 14x^(2) - 19x - 8 is divided by 4x+ 3 then find the quotient and the remainder.

If the polynomials x ^(3) + ax ^(2) + 5 and x ^(3) - 2x ^(2)+a are divided by (x +2) leave the same remainder. Find the value of a.

When a polynomial 2x ^(3) + 3x ^(2) + ax + b is divided by (x-2) leaves remainder 2, and (x +2) leaves remainder -2. Find a and b.

Find the remainder when f (x) =x ^(4) - 3x ^(2) + 4 is divided by g (x) =x -2 and verify the result by actual division .

A certain polynomial P(x), x in R when divided by x-a ,x-b and x-c leaves remainders a , b , and c , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c) where a, b, c are distinct.

A certain polynomial P(x)x in R when divided by x-a ,x-ba n dx-c leaves remainders a , b ,a n dc , resepectively. Then find remainder when P(x) is divided by (x-a)(x-b)(x-c)w h e r eab, c are distinct.

Find the remainder when p (x) = x ^(3) - 6x ^(2) + 14x -3 is divided b y g (x) =1-2x and verify the result by long division.