Polynomials

Identify the remainder when x^3 + 1 is divided by x + 1.

Factorize x^2 + 7x + 12.

What is the value of k if x-1 is a factor of x^2 + kx - 5?

Expand (x + 2)(x^2 - 2x + 4).

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

Simplify (2x^2 + 4x) / 2x.

If the roots of x^2 - px + q = 0 are 2 and 3, find p.

Find the value of p if x = -1 is a zero of P(x) = px^2 - 2x + 3.

What is the product of (x + a)(x + b)?

If x^2 - 1 is a factor of x^4 + ax^3 + bx^2 + cx + d, what must be true?

Factorize 3x^2 - 12.

What is the degree of a polynomial with 5 terms?

Simplify (x+1)^2 - x^2.

If P(x) = x^2 - 5x + 4, find P(4).

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

If x - a is a factor of x^n - a^n for all positive integers n, find the remainder.

Find the value of k if x + 2 is a factor of 2x^3 + 5x^2 + kx + 10.

What is the HCF of x^3 - 1 and x^2 + x + 1?

Factorize completely: x^4 - 13x^2 + 36.

Find the LCM of x^2 - y^2 and x^3 - y^3.