Question Bank

Using synthetic division, find the remainder when x^3 - 2x^2 + 3x - 5 is divided by x - 2.

If the HCF of two expressions is (x - 3) and their LCM is (x^2 - 9)(x + 2), and one expression is (x^2 - 9), find the other.

Factorize: x^3 - 8.

If f(x) = 2x^2 - 3x + 1, find the value of f(x+1).

Find the LCM of (a^2 - b^2) and (a^3 - b^3).

What must be added to x^2 + 6x to make it a perfect square?

Find the quotient when x^2 - 7x + 12 is divided by x - 3.

If (x - k) is the HCF of x^2 - x - 6 and x^2 + 3x + 2, find k.

The degree of the product (x^2 + 1)(x^3 - x + 1)(x + 5) is:

Factorize: x^2 + 1/x^2 + 2.

If x + y = 5 and xy = 6, find the value of x^3 + y^3.

Solve for x: x^2 - 4x = 0.

Which value of x makes x^2 - 1 / (x-1) undefined?

If P(x) is a polynomial of degree 4, and it is divided by a polynomial of degree 2, what is the degree of the quotient?

The sum of the zeros of the polynomial x^2 - 7x + 10 is:

Find the value of k if the remainder is 5 when x^2 + kx + 7 is divided by x - 1.

Simplify: (x + 2)(x^2 - 2x + 4).

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

What are the factors of 6x^2 - x - 2?

The product of zeros of x^2 - 4x + 3 is: