Practice Polynomials and Remainder Theorem Practice Questions with Detailed Solutions – Level 2

What is the remainder when \(p(x)\) \({}= 2x^{3} - 5x^{2} + 4x - 7\) is divided by \((x - 3)?\)

If \((x + 2)\) is a factor of \(x^{3} + kx^{2} - 4x - 12,\) what is the value of \(k?\)

If \(\alpha\) and \(\beta\) are the zeroes of the polynomial \(3x^{2} - 7x + 2,\) what is the value of \(\alpha^{2} + \beta^{2}?\)

What is the degree of the polynomial \((x^{3} - 2x + 1)(4x^{2} + 3)^{2}?\)

Which of the following is the correct factorisation of \(x^{3} - 2x^{2} - 5x + 6?\)

What is the LCM of \(x^{2} - 9\) and \(x^{2} + x - 6?\)

When \(x^{3} + ax + b\) is divided by \((x - 1),\) the remainder is 4, and when it is divided by \((x + 1),\) the remainder is 8. What is the value of \(a?\)

Which of the following is a quadratic polynomial whose zeroes are \(2 + \sqrt{3}\) and \(2 - \sqrt{3}?\)

What is the remainder when \(4x^{3} - 2x^{2} + 6x + 5\) is divided by \((2x - 1)?\)

If \((x - 1)\) and \((x + 2)\) are both factors of \(x^{3} + px^{2} + qx - 6,\) what are the values of \(p\) and \(q?\)