A polynomial of degree 2 in x , when divided by `(x+1),(x+2)and(x+3)`, leaves remainders 1 , 4 and 3 respectively . Find the polynomial.

The polynomial f (x)= x^4 + 2 x^3 + 3 x^2 - ax + b when divided by (x-1) and (x + 1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when f (x) is divided by (x-2)

Find the quadratic polynomial when divided by x, x -1 and x -2 leaves remainders 1, 2 and 9 respectively

Find a linear polynomial which when divided by (2x+1)and(3x+2) leaves remainders 3 and 4, respectively.

The polynomials f(x)=x^4-2x^3+3x^2-ax+b when divided by (x-1) and (x+1) leaves remainder 5 and 19 respectively. Find the value of a and b hence, find the remainder when f(x) is divided by (x-2)

The polynomials f(x)=x^(4)-2x^(3)+3x^(2)-ax+b when divided by (x-1) and (x+1) leaves the remainders 5 and 19 respectively.Find the values of a and b..Hence,find 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.