1. Factorise x² + 5x + 6.
- (x+1)(x+6)
- (x−2)(x−3)
- (x+2)(x+3)
Check the answer and reasoning
(x+2)(x+3)
The constants multiply to 6 and add to 5.
MATH / IGCSE
Algebra, equations and sequences
Expanding distributes multiplication over addition; factorising reverses the process. Linear and quadratic equations, inequalities and simultaneous equations express constraints.
Learning objectives
- Explain algebra, equations and sequences using a concrete example.
- Apply the worked method and justify each step.
- Recognise the limitation described in the final check.
The big idea
Expanding distributes multiplication over addition; factorising reverses the process. Linear and quadratic equations, inequalities and simultaneous equations express constraints.
Arithmetic sequences have a constant difference. Rearrange a formula using inverse operations, and check solutions in the original equation, especially after division by an expression containing the unknown.
Equations and relationships
The distributive law.
Worked example
Solve 3x + 5 = 20.
Follow the solution
Subtract 5 from both sides to get 3x = 15, then divide by 3.
Investigate and explain
Predict the worked result before calculating. Change one input, record the new result, and explain which assumptions still hold.
Related interactive model. Compare its assumptions with the explanation; it is not a complete syllabus lesson.
Check your understanding
2. Solve 3x + 5 = 20.
- x = 5
- x = 15
- x = 25/3
Check the answer and reasoning
x = 5
Subtract 5 from both sides to get 3x = 15, then divide by 3.
3. When multiplying an inequality by −1, what happens?
- Keep its direction always
- Reverse its direction
- Replace it with equality
Check the answer and reasoning
Reverse its direction
Negation reverses order: 2 < 3 becomes −2 > −3.