Given `ax^(2)+bx+c` is a quadratic polynomial in x and leaves remainders 6 , 11 and 18 , respectively, when divided by `(x+1), (x+2)and(x+3)`. Find the value of a + b + c.

A quadratic polynomial in x leaves remainders 4 , 4 and 0 , respectively when divided by (x-1),(x-2) and (x-3) . Find the quadratic polynomial.

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

A quadratic polynomial in x leaves remainders as 4 and 7 respectively when divided by (x+1) and (x-2) . Also it is exactly divisible by (x-1) . Find the quadratic polynomial.

Polynomial x^3-ax^2+bx-6 leaves remainder -8 when divided by x-1 and x-2 is a factor of it. Find the values of 'a' and 'b'.

The polynomials 2x^3- 7x^2 + ax -6 and x^3-8x^2 +(2a + 1)x- 16 leave the same remainder when divided by x- 2. Find the value of a

Let p(x) be a quadratic polynomial suchthat p(0)=1. If p(x) leaves remainder 4 when divided by x-1 and it leaves remainder 6 when divided by x+1; then

Let P(x)=x^(2)+bx+c be a quadratic polynomial with real coefficients such that int_(0)^(1)P(x)dx=1 and P(x) leaves remainder 5 when it is divided by (x - 2). Then the value of 9(b + c) is equal to:

Given that the polynomial (x^2 + ax + b) leaves the same remainder when divided by (x -1) or (x + 1 ). What are the values of a and b respectively ?

The expression 2x^3+ ax^2+ bx -2 leaves remainder 7 and 0 when divided by 2x- 3 and x+ 2 respectively. Calculate the values of a and b.