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 x^(5) is divided by x^(3)-4x

A polynomial f(x) when divided by (x-5)and (x-7) leaves remainders 6 and 16 , respectively. Find the remainder when f(x) is divided by (x-5)(x-7) .

When polynomial f(x) is divided (x-1) and (x-2) it leaves remainder 5 and 7 respectively.What is the remainder when f(x) is divided by (x-1)(x-2)?

If p(x)=x^4-3x^2-ax+b is a polynomial such that when it is divided by x-1 and x+1, the remainders are 5 and 19 respectively. Then find the remainder when p(x) is divided by (x-2)

If f(x) = x^4 - 2 x^3 + 3 x^2 - ax +b a polynomial such that when it is divided by (x-1) and (x+1); the remainders are 5 and 19 respectively. Determine the remainder when f(x) is divided by (x-2).

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.

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.

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.

Given f(x) is a cubic polynomial in x .If f(x) is divided by (x+3),(x+4),(x+5) and (x+6), then it leaves the remainders 0,0,4 and 6 respectively.Find the remainder when f(x) is dividedby x+7.

If f(x)=x^4-2x^3+3x^2-a x+b is a polynomial such that when it is divided by x-1 and x+1 , remainders are 5 and 19 respectively. Determine the remainder when f(x) is divided by x-3.