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Grade 9 Math — Factorisation

Break an algebraic expression into factors, and use those factors to divide one expression by another.

Name: ________________________

  1. 1.What is the highest common factor of the two terms in 12x + 18?

  2. 2.Sort each expression by the method that factorizes it.

    Groups: Take out a common factor · Use a² - b² = (a - b)(a + b)

    • 7x + 21
    • 9a² - 4b²
    • 12m + 18n
    • x² - 1
    • 5y² - 15y
    • x² - 25

  3. 3.x² + 7x + 12 factorizes as (x + 3)(x + ?). What number belongs in place of the question mark?

  4. 4.Take a out of a² + ab as a common factor. What is left inside the bracket?

  5. 5.Which of these is x² + 10x + 25 written in factorized form?

    • a) (x + 5)²
    • b) (x + 10)²
    • c) (x + 5)(x - 5)
    • d) (x + 25)(x + 1)

  6. 6.Which of these is 4x² - 9 written in factorized form?

    • a) (2x - 3)(2x - 3)
    • b) (4x - 3)(x + 3)
    • c) (2x - 9)(2x + 1)
    • d) (2x - 3)(2x + 3)

  7. 7.Put these expressions in order by the highest common factor of their terms, smallest first.

    • 14x + 21
    • 6x + 18
    • 10x + 25
    • 4x + 8
    • 3x + 9

  8. 8.Match each expression to its factorized form.

    • x² - 16
    • x² + 8x + 16
    • 3x + 12
    • x² - 4x
    • 2x² - 32
    • (x + 4)²
    • (x - 4)(x + 4)
    • x(x - 4)
    • 3(x + 4)
    • 2(x - 4)(x + 4)

Answer key — Grade 9 Math — Factorisation

  1. 1. 6
  2. 2. 7x + 21 → Take out a common factor; x² - 25 → Use a² - b² = (a - b)(a + b); 5y² - 15y → Take out a common factor; 9a² - 4b² → Use a² - b² = (a - b)(a + b); 12m + 18n → Take out a common factor; x² - 1 → Use a² - b² = (a - b)(a + b)
  3. 3. 4
  4. 4. a + b
  5. 5. a) (x + 5)²
  6. 6. d) (2x - 3)(2x + 3)
  7. 7. 1. 3x + 9 2. 4x + 8 3. 10x + 25 4. 6x + 18 5. 14x + 21
  8. 8. x² - 16 → (x - 4)(x + 4); x² + 8x + 16 → (x + 4)²; 3x + 12 → 3(x + 4); x² - 4x → x(x - 4); 2x² - 32 → 2(x - 4)(x + 4)