Let `f(x) and g(x)` be polynomials with real coefficients. If `F(x)=f(x^3)+xg(x^3)` is divisible by `x^2+x+1`, then both `f(x) and g(x)` are divisible by

If f(x) = g(x)^3+xh(x)^3 is divisible by x^2+x+1 , then

Let P(x) and Q(x) be two polynomials.Suppose that f(x) = P(x^3) + x Q(x^3) is divisible by x^2 + x+1, then (a) P(x) is divisible by (x-1),but Q(x) is not divisible by x -1 (b) Q(x) is divisible by (x-1), but P(x) is not divisible by x-1 (c) Both P(x) and Q(x) are divisible by x-1 (d) f(x) is divisible by x-1

If f(x) and g(x) are two polynomials such that the polynomial P(x)=f(x^(3))+g(x^(3)) is divisible by x^(2)+x+1 , then P(1) is equal to ........

Let f(x) and g(x) be two polynomials (with real coefficients) having degrees 3 and 4 respectively. What is the degree of f(x)g(x)?

If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(x^3)+x^2g(x^6) is divisible by x^2+x+1, then f(1)=g(1) (b) f(1)=1g(1) h(1)=0 (d) all of these

If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(x^(3))+x^(2)g(x^(6)) is divisible by x^(2)+x+1, then ( a )f(1)=g(1) (b) f(1)=1g(1)( ) h(1)=0 (d) all of these

Let f(x) be a polynomial with real coefficients such that f(0)=1 and for all x ,f(x)f(2x^(2))=f(2x^(3)+x) The number of real roots of f(x) is:

Let f(x) be a polynomial function: f(x)=x^(5)+ . . . . if f(1)=0 and f(2)=0, then f(x) is divisible by

If the polynomial f(x)=ax^3+bx-c is divisible by g(x)=x^2+bx+c ,then the value of ab is

Let f(x) be a polynomial of degree 6 divisible by x^(3) and having a point of extremum at x = 2 . If f'(x) is divisible by 1 + x^(2) , then find the value of (3f(2))/(f(1)) .