If a polynomial f (x) is divided by ` (x - 3) and (x - 4)` it leaves remainders as 7 and 12 respectively, then find the remainder when f (x) is divided by `(x-3)(x-4)`.

Find the remainder when 27^(40) is divided by 12.

Find the remainder when x ^(3) +1 devided by (x +1)

Consider an unknow polynomial which divided by (x - 3) and (x-4) leaves remainder 2 and 1, respectively. Let R(x) be the remainder when this polynomial is divided by (x-3)(x-4) . If equations R(x) = x^(2)+ ax +1 has two distint real roots, then exhaustive values of a are.

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.

Consider an unknow polynomial which divided by (x - 3) and (x-4) leaves remainder 2 and 1, respectively. Let R(x) be the remainder when this polynomial is divided by (x-3)(x-4) . If R(x) = px^(2) + (q-1) x + 6 has no distinct real roots and p gt 0 , then the least value of 3p + q is

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 x^3+4x^2-7x+6 is divided by x-1.

What is the remainder when x^(2018) + 2018 is divided by x-1 .