Polynomials

If x + 1/x = 4, find x^2 + 1/x^2.

Solve for x: x^3 - 6x^2 + 11x - 6 = 0.

Find the remainder when x^3 - kx^2 + 6x - k is divided by x - k.

If P(x) is divided by (x - a)(x - b), what is the general form of the remainder?

If a + b + c = 0, find the value of a^3 + b^3 + c^3.

Simplify: [ (x^2 - 1) / (x^2 - 2x + 1) ] * [ (x - 1) / (x + 1) ].

Find the HCF of x^4 + x^2 + 1 and x^2 + x + 1.

If x^2 - 3x + 2 is a factor of x^4 - px^2 + q, find p.

Find the values of a and b if x^2 - 1 is a factor of ax^4 + bx^3 + 1.

If f(x) = x^2 - 5x + 7, find f(x+1) - f(x).

What is the remainder when x^3 + 3x^2 + 3x + 1 is divided by x + 1?

Find the HCF of x^2 - 4, x^2 - 5x + 6, and x^2 - 4x + 4.

Find the LCM of 4(x+1)^2 and 6(x^2-1).

If x = 1 is a double root of x^3 - 3x + 2, it means:

Factorize a^4 + a^2b^2 + b^4.

Find the value of x^3 + y^3 if x+y=5 and xy=6.

Divide x^4 - y^4 by x - y.

Find k if x+1 is a factor of x^10 + k.

What is the degree of a polynomial resulting from the division of degree 7 by degree 3?

Solve: (x-1)(x-2) = (x-1)(2x-3).