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Year 11 Maths — Polynomials

Find the degree of a polynomial, evaluate it at a value and recognise its zeroes.

Name: ________________________

  1. 1.What is the degree of the polynomial 5x + 1?

  2. 2.Sort each polynomial by its degree.

    Groups: Linear · Quadratic

    • 3x + 2
    • 5 - x
    • 9x² + 4
    • x² + 1
    • x
    • 2x² - 7x

  3. 3.Match each polynomial to its degree.

    • 7
    • 4x + 1
    • x² - 3
    • 2x³ + x
    • x⁵
    • 5
    • 3
    • 1
    • 0
    • 2

  4. 4.If p(x) = x² - 5x + 6, what is p(3)?

  5. 5.The factor theorem says that if p(k) = 0 then (x - k) is a factor of p(x). Given that p(2) = 0, what is k?

  6. 6.If p(x) = 2x + 6, what value of x makes p(x) = 0?

  7. 7.If p(x) = x³ - 2x² + x, what is p(1)?

  8. 8.What is the degree of the polynomial 3x⁴ + 2x - 7?

Answer key — Year 11 Maths — Polynomials

  1. 1. 1
  2. 2. 3x + 2 → Linear; 5 - x → Linear; x → Linear; x² + 1 → Quadratic; 2x² - 7x → Quadratic; 9x² + 4 → Quadratic
  3. 3. 7 → 0; 4x + 1 → 1; x² - 3 → 2; 2x³ + x → 3; x⁵ → 5
  4. 4. 0
  5. 5. 2
  6. 6. -3
  7. 7. 0
  8. 8. 4