Practice Polynomials and Remainder Theorem Practice Questions with Detailed Solutions – Level 1

What is the degree of the polynomial \((x^{2} + 1)(x^{3} - 2x)?\)

What is the remainder when \(x^{3} - 2x^{2} + 4x - 5\) is divided by \((x - 2)?\)

If \((x - 3)\) is a factor of \(x^{2} + kx - 12,\) what is the value of \(k?\)

Which of the following is the correct factorisation of \(x^{2} - 7x + 12?\)

What is the sum of the zeroes of the polynomial \(2x^{2} - 8x + 5?\)

What is the product of the zeroes of the polynomial \(3x^{2} + 5x - 12?\)

What is the HCF of \((x^{2} - 4)\) and \((x^{2} + 5x + 6)?\)

What are the zeroes of the polynomial \(x^{2} - 2x - 15?\)

What is the remainder when \(x^{4} + x^{3} - 2x + 7\) is divided by \((x + 1)?\)

Which of the following is a factor of \(x^{3} - 6x^{2} + 11x - 6?\)