Grade 10 Maths · Algebra

Factorise a trinomial

Factorise x² + bx + c using two numbers that multiply to c and add to b (for example x² + 5x + 6 = (x + 2)(x + 3)).

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Gr 9 Factorisation: Trinomials IntroductionKevinmathscience

Gr 9 Factorisation: Trinomials PracticeKevinmathscience

Factorising Trinomials Grade 10 PART 2 Taking out a HCF firstMiss Martins Maths and Science

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Question 9.2 · May/June 2025 · Paper 1 · National (DBE) · 4 marks

Given:

f (x) = x^{3} - 6 x^{2} + 9 x - 4 = (x - 4) (x - k)^{2}

9.2 Calculate the coordinates of the turning points of

f

.(4)

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More past paper questions: factorise a trinomial

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3. Question 1.1.1 · May/June 2025 · Paper 1 · National (DBE) · 3 marks
1.1 Solve for $x$ :
1.1.1 $x^{2} - 3 x - 10 = 0$ (3)
Show the memo (2 ticks)Memo
1. ✓
  Factorise the quadratic equation $(x + 2) (x - 5) = 0$
  1 mark · Factorise a trinomial
2. ✓
  Solve for x $x = - 2$ or $x = 5$
  2 marks · Solve a quadratic by factorising
4. Question 1.3.1 · March 2025 · Provincial · 2 marks
1.3 Factorise the following expressions fully.
1.3.1 $x^{2} - 3 x - 10$ (2)
Show the memo (1 tick)Memo
1. ✓
  Find factors of -10 that add to -3 $(x + 2) (x - 5)$
  2 marks · Factorise a trinomial
5. Question 2.1.2 · March 2022 · Provincial · 2 marks
2.1 Factorize completely:
2.1.2 $x^{2} - 4 x + 3$ (2)
Show the memo (1 tick)Memo
1. ✓
  Trinomial factorization $(x - 3) (x - 1)$
  2 marks · Factorise a trinomial
6. Question 1.1.3 · November 2024 · Paper 1 · National (DBE) · 4 marks
1.1 Solve for $x$ :
1.1.3 $x^{2} - 2 x - 3 > 0$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Factorise the inequality $(x - 3) (x + 1) > 0$
  1 mark · Factorise a trinomial
2. ✓
  Identify critical valuesCritical values: $x = 3$ or $x = - 1$
  1 mark · Solve a quadratic by factorising
3. ✓
  Determine the range $x < - 1$ or $x > 3$
  OR
  $x \in (- \infty; - 1) \cup (3; \infty)$
  2 marks · Solve a quadratic inequality

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