If `x-c` is a factor of order m of the polynomial `f(x)` of degree n `(1 < m < n)`, then find the polynomials for which `x=c` is a root.

If x-r is a factor of the polynomial f(x)=a_0x^n+a_1x^(n-1)+.....+a_n repeated m times, (1ltxlt=n), then r is a root of f^(prime)(x)=0 repeated m times.

A polynomial equation in x of degree n always has :

Determine whether (x-1) is a factor of the following polynomials : x^(4) + 5x^(2) - 5x +1

If x^(2) + x + 1 is a factor of the polynomial 3x^(3) + 8x^(2) + 8x + a, then find the value of a.

p(x) is a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) xx q(x) is ?

Determine whether (x-1) is a factor of the following polynomials : x^(3) + 5x^(2) - 10x + 4