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WAEC Further Mathematics questions: Polynomials and the remainder theorem

16 questions with answers and explanations. Tap an option to check yourself.

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All topicsCoordinate geometry and conic sections · 16Differentiation · 18Dynamics · 15Functions and rational functions · 15Integration · 16Matrices and determinants · 16Permutations and combinations · 15Polynomials and the remainder theorem · 16Probability · 16Sequences and series · 16Sets, binary operations and logic · 16Statics · 14Statistics · 15Surds, indices and logarithms · 16The binomial theorem · 15Trigonometry · 16Vectors · 16

  1. Question 1· Polynomials and the remainder theorem· WAEC

    The sum of the roots of 2x² − 6x + 1 = 0 is

    Explanation and discussion

  2. Question 2· Polynomials and the remainder theorem· WAEC

    (x − 2) is a factor of x³ − 3x² + kx + 2. Find k.

    Explanation and discussion

  3. Question 3· Polynomials and the remainder theorem· WAEC

    The remainder when x³ − 2x + 1 is divided by (x − 2) is

    Explanation and discussion

  4. Question 4· Polynomials and the remainder theorem· WAEC

    Find the discriminant of x² + 4x + 5.

    Explanation and discussion

  5. Question 5· Polynomials and the remainder theorem· WAEC

    If (x + 1) is a factor of x² + kx + 3, the value of k is

    Explanation and discussion

  6. Question 6· Polynomials and the remainder theorem· WAEC

    Find the range of values of x for which x² − 5x + 6 < 0.

    Explanation and discussion

  7. Question 7· Polynomials and the remainder theorem· WAEC

    Find the remainder when 2x³ + x² − 5x + 7 is divided by (x + 2).

    Explanation and discussion

  8. Question 8· Polynomials and the remainder theorem· WAEC

    If α and β are the roots of x² − 5x + 6 = 0, find α² + β².

    Explanation and discussion

  9. Question 9· Polynomials and the remainder theorem· WAEC

    For what values of k does x² + kx + 9 = 0 have equal roots?

    Explanation and discussion

  10. Question 10· Polynomials and the remainder theorem· WAEC

    Find the quotient when x³ − 1 is divided by x − 1.

    Explanation and discussion

  11. Question 11· Polynomials and the remainder theorem· WAEC

    The sum of the roots of the equation 2x² − 7x + 3 = 0 is

    Explanation and discussion

  12. Question 12· Polynomials and the remainder theorem· WAEC

    α and β are the roots of x² − 4x + 1 = 0. Find 1/α + 1/β.

    Explanation and discussion

  13. Question 13· Polynomials and the remainder theorem· WAEC

    If (x + 1) is a factor of x³ + kx² − x − 2, find the value of k.

    Explanation and discussion

  14. Question 14· Polynomials and the remainder theorem· WAEC

    Find the quadratic equation whose roots are 3 and −5.

    Explanation and discussion

  15. Question 15· Polynomials and the remainder theorem· WAEC

    The roots of a quadratic equation are real and equal when the discriminant is

    Explanation and discussion

  16. Question 16· Polynomials and the remainder theorem· WAEC

    The product of the roots of 3x² + 5x − 12 = 0 is

    Explanation and discussion

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