Lesson B6

B6 Polynomials, algebraic division and the factor theorem Quiz: AQA Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson B6, Polynomials, algebraic division and the factor theorem: 20 multiple choice questions for the AQA Maths (7357), Unit 2: Algebra and functions, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. Expand (2x - 1)(x + 4).

    • 2x^2 + 9x - 4
    • 2x^2 + 7x + 4
    • 2x^2 - 7x - 4
    • 2x^2 + 7x - 4

  2. What does the factor theorem state?

    • If f(a) = 0 then (x - a) is a factor of f(x)
    • If (x - a) is a factor then f(a) = a
    • If f(a) = 1 then (x - a) is a factor of f(x)
    • If f(-a) = 0 then (x - a) is a factor of f(x)

  3. What is the remainder when a polynomial f(x) is divided by (x - a)?

    • f(a)
    • a f(0)
    • f'(a)
    • f(-a)

  4. Factorise x^3 - 6x^2 + 11x - 6 fully.

    • (x - 1)(x - 2)(x - 3)
    • (x - 1)(x + 2)(x - 3)
    • (x - 1)(x - 2)(x + 3)
    • (x + 1)(x + 2)(x + 3)

  5. Which of these is a factor of x^3 + 2x^2 - x - 2?

    • (x^2 + 2)
    • (x - 2)
    • (x + 3)
    • (x + 2)

  6. What is the remainder when x^3 + 2x^2 - 5 is divided by (x - 2)?

    • 11
    • 16
    • 3
    • -5

  7. For what value of k is (x - 2) a factor of x^3 - kx + 6?

    • k = 5
    • k = 14
    • k = -7
    • k = 7

  8. Divide 2x^3 + 3x^2 - 5x + 1 by (x + 2). What are the quotient and remainder?

    • Quotient 2x^2 - 3x + 1, remainder 7
    • Quotient 2x^2 - x - 3, remainder 7
    • Quotient 2x^2 - x - 3, remainder -7
    • Quotient 2x^2 + x - 3, remainder 7

  9. Simplify (x^2 - 9)/(x^2 + x - 6).

    • (x + 3)/(x - 2)
    • (x - 3)/(x - 2)
    • (x - 3)/(x + 2)
    • (x - 3)(x + 2)

  10. Which expression is NOT a polynomial?

    • x^2 - 3
    • 3x^3 + 1
    • 1/x + 2
    • x^4 - x

  11. Find a and b so that x^3 + ax^2 + bx - 6 has both (x - 1) and (x - 2) as factors.

    • a = -6, b = 11
    • a = 5, b = 0
    • a = 6, b = -1
    • a = -6, b = -11

  12. Simplify (x^3 - 1)/(x - 1) for x not equal to 1.

    • x^2 + x - 1
    • x^2 - x + 1
    • x^2 + x + 1
    • x^2 + 1

  13. What is the coefficient of x^2 in the expansion of (x + 3)(x^2 - 2x + 1)?

    • 3
    • -5
    • 1
    • -2

  14. Simplify 3a^2b - 2ab^2 + 5a^2b + ab^2.

    • 6a^2b - ab^2
    • 8a^2b - 3ab^2
    • 8a^2b - ab^2
    • 8a^2b + ab^2

  15. Factorise 8x^3 - 27 fully.

    • (2x - 3)(4x^2 + 6x + 9)
    • (2x + 3)(4x^2 - 6x + 9)
    • (2x - 3)(4x^2 - 6x + 9)
    • (2x - 3)(4x^2 + 6x - 9)

  16. For f(x) = x^3 - 4x^2 + kx + 6, the remainder is zero when divided by (x + 1). What is k?

    • k = 11
    • k = 1
    • k = -1
    • k = 5

  17. Factorise x^3 - 7x + 6 fully.

    • (x - 1)(x + 2)(x + 3)
    • (x - 1)(x - 2)(x + 3)
    • (x - 1)(x - 2)(x - 3)
    • (x + 1)(x - 2)(x - 3)

  18. What is the remainder when x^4 + 1 is divided by (x + 1)?

    • 1
    • 2
    • -2
    • 0

  19. What is the degree of the remainder when a polynomial is divided by a linear divisor?

    • Equal to the degree of the quotient
    • Zero, so the remainder is a constant
    • Equal to the degree of the dividend
    • One, so the remainder is linear

  20. Given that (x + 2) is a factor of x^3 + kx^2 - 4x + 4, find k.

    • k = 1
    • k = -3
    • k = -1
    • k = 3

All AQA Maths quizzes