Polynomials

Find the LCM of x^2 - 1 and x^2 - 2x + 1.

If x - 2 is a factor of x^2 + ax + 2b and a + b = 1, find the values of a and b.

The expression x^4 + 4 can be factorized as:

Find the HCF of x^3 - 1, x^4 + x^2 + 1, and x^2 - 1.

If α and β are the zeros of the polynomial 2x^2 - 5x + 7, find the value of 1/α + 1/β.

If x^2 - 1 is a factor of ax^4 + bx^3 + cx^2 + dx + e, then:

What is the remainder when x^100 - 1 is divided by x^2 - 3x + 2?

Factorize: a^3 + b^3 + c^3 - 3abc.

If x + 1/x = 3, find the value of x^5 + 1/x^5.

Find the HCF of (x^2-1), (x^2-2x+1) and (x^3-1).

If the roots of the equation x^2 - px + q = 0 differ by unity, then:

Factorize: x^4 + x^2y^2 + y^4.

If (x - 1) and (x + 2) are factors of x^3 + ax^2 + bx - 2, find a and b.

The LCM of x^2 - xy, x^2y - xy^2, and xy - y^2 is:

If f(x) = x^3 - 3x^2 + 4x - 5, find the value of f(x) + f(-x).

Which of the following polynomials has (x + 1) as a factor?

Simplify the rational expression: (x^2 - 5x + 6) / (x^2 - 4).

If x^2 + px + q and x^2 + mx + n have a common factor (x - a), then a is:

The remainder when P(x) = 4x^3 - 3x^2 + 2x - 1 is divided by (2x - 1) is:

Find the value of (x-a)^3 + (x-b)^3 + (x-c)^3 if a+b+c = 3x.