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

Let P(x) be a polynomial of degree at most 5 which leaves remainders -1 and 1 upon divison by (x-1)^(3) and (x+1)^(3) , respectively. The sum of pairwise product of all roots ( real and complex) of P(x)=0 is

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

Let a!=0 and p(x) be a polynomial of degree greater than 2. If p(x) leaves reminders a and -a when divided respectively, by x+a and x-a , then the remainder when p(x) is divided by x^2-a^2 is

Let a ne 0 and P(x) be a polynomial of degree greater then 2.If P(x) leaves remianders a and a- when divided, respectively, by x + a and x - a, then find the remainder when P(x) is divided by x^(2) - a^(2) .

Let a ne 0 and p(x ) be a polynomial of degree greater than 2. If P(x ) leaves remainder a and -a when divided respectively by x+a and x-a then the remainder when p(X ) is divided by x^2 -a^2 is