Lesson 1.02j

1.02j Polynomials and rational expressions Quiz: OCR Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.02j, Polynomials and rational expressions: 20 multiple choice questions for the OCR Maths (H240), Unit 2: Algebra and Functions, written with Revision Ninja.

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The 20 questions

  1. If f(a) = 0 for a polynomial f, which expression is a factor of f(x)?

    • f(a)
    • (a x)
    • (x + a)
    • (x - a)

  2. What does the remainder theorem say about dividing f(x) by (x - a)?

    • The remainder is f(-a)
    • The remainder is f(a)
    • The remainder is f(a)/a
    • The remainder is a f(0)

  3. Given f(x) = x^3 - 2x^2 - 5x + 6, what is the quadratic quotient when divided by (x - 1)?

    • x^2 + x - 6
    • x^2 - 3x + 2
    • x^2 - x - 6
    • x^2 - x + 6

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

    • -1
    • -11
    • 5
    • 11

  5. Simplify (x^2 - 9)/(x + 3).

    • x + 3
    • (x - 3)/(x + 3)
    • x - 9
    • x - 3

  6. Factorise x^2 - 5x + 6.

    • (x - 2)(x - 3)
    • (x - 1)(x - 6)
    • (x - 2)(x + 3)
    • (x + 2)(x + 3)

  7. Is (x + 1) a factor of x^3 + x^2 + x + 1?

    • Yes, because f(-1) = 0
    • No, because f(-1) = 4
    • No, because f(1) = 0
    • Yes, because f(1) = 4

  8. Expand (x + 2)(x^2 - x + 1).

    • x^3 + x^2 + x + 2
    • x^3 - x^2 + x + 2
    • x^3 + x^2 - x + 2
    • x^3 + 3x^2 - x + 2

  9. Simplify (x^2 + 4x + 3)/(x^2 - 1).

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

  10. Divide 2x^2 + 3x - 5 by (x - 1). What is the quotient?

    • 2x + 5 + 1/(x - 1)
    • 2x + 5
    • 2x - 5
    • 2x + 3

  11. Factorise x^3 - 8 completely.

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

  12. Solve x^3 - 6x^2 + 11x - 6 = 0.

    • x = 2, 3, 6
    • x = 1, 2, -3
    • x = -1, -2, -3
    • x = 1, 2, 3

  13. Find k so that (x - 2) is a factor of x^3 - kx^2 + 2x + 4.

    • k = -4
    • k = 4
    • k = 2
    • k = 6

  14. What is the remainder when x^4 + x^2 + 1 is divided by (x - 1)?

    • 2
    • 1
    • 3
    • 0

  15. Simplify (x^2 - 4)/(x^2 - 5x + 6) times (x - 3)/(x + 2), with x not equal to 2, 3 or -2.

    • 1
    • x - 2
    • 0
    • (x - 2)/(x + 2)

  16. How many roots, counting multiplicity, can a cubic polynomial have at most?

    • Two
    • One
    • Four
    • Three

  17. What is the solution set of (x^2 - 3x + 2)/(x - 1) = 0?

    • {1, 2}
    • {}
    • {2}
    • {1}

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

    • 4
    • 2
    • -2
    • -4

  19. Find a so that (x - 1) and (x + 2) are both factors of x^3 + ax^2 - 5x + 6.

    • a = 2
    • a = 3
    • a = -2
    • a = -1

  20. Find the remainder when 2x^3 - 3x^2 + x + 4 is divided by (2x - 1).

    • 4
    • 3.5
    • 2
    • 1

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