Find a quadratic polynomial divisible by `(2x - 1) and (x + 3)` and which leaves remainder 12 on division by `(x - 1).`

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

If lx^(2)+mx+n is exactly divisible by (x - 1 ) and (x + 1) and leaves a remainder 1 when divided by x + 2 , then find m and n .

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

Given that px^(2)+qx+6 leaves the remainder as 1 on division by 2x=1 and 2qx^(2)+6x+p leaves the remainder as 2 on division by 3x-1 . Find p and q .

If the quadratic polynomial p(x) is divisible by x - 4 and 2 is a zero of p(x) then find the polynomial p(x).

Given that ax^2+bc+6 leaves the remainder 1 on division by 2x+1 and 2bx^2+6x+a leaves the remainder 2 on divisible by 3x-1. find a and b.

p(x) be a polynomial of degree at most 5 which leaves remainder - 1 and 1 upon division by (x-1)^3 and (x+1)^3 respectively, the number of real roots of P(x) = 0 is

p(x) be a polynomial of degree at most 5 which leaves remainder -1and 1upon division by (x-1)^(3) and (x+1)^(3) respectively,the number of real roots of P(x)=0 is

p(x) be a polynomial of degree at most 5 which leaves remainder - 1 and 1 upon division by (x-1)^3 and (x+1)^3 respectively, the number of real roots of P(x) = 0 is