Factorising quadratics
Maths, Algebra. Usually met in years 9 to 11.
Factorise expressions, from taking out a common factor to quadratics and the difference of two squares.
What you practise
- Taking out a common factor
- Factorising x² + bx + c
- The difference of two squares
Ends with quadratics where the x² term has a number in front. Practice moves up a level when a round goes well and down when it does not.
Sample questions
Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.
Sample question, level 2 of 5
Factorise x² + 24x + 144.
- (x + 12)(x − 12)
- (x + 24)(x + 144)
- (x − 12)(x − 12)
- (x + 12)(x + 12)
- (x + 13)(x + 12)
Show the answer and method
Answer: D, (x + 12)(x + 12)
The method: Find two numbers that multiply to 144 and add to 24: 12 and 12. So (x + 12)(x + 12).
Why the other options are wrong:
- A, (x + 12)(x − 12): One sign is wrong: the numbers multiply to a positive, so they have the same sign.
- B, (x + 24)(x + 144): The middle and last numbers were used directly. Find two numbers that multiply to 144 and add to 24.
- C, (x − 12)(x − 12): The signs are wrong: check by expanding. Both numbers must add to give +24.
- E, (x + 13)(x + 12): Close, but the numbers do not multiply to the last term.
Sample question, level 4 of 5
Factorise x² − 361.
- (x + 19)(x + 19)
- (x − 361)(x + 361)
- (x − 19)(x + 19)
- x(x − 19)
- (x − 19)(x − 19)
Show the answer and method
Answer: C, (x − 19)(x + 19)
The method: This is a difference of two squares: x² − 19². It factorises to (x − 19)(x + 19).
Why the other options are wrong:
- A, (x + 19)(x + 19): This expands to x² + 38x + 361.
- B, (x − 361)(x + 361): 361 was used instead of its square root, 19.
- D, x(x − 19): This does not expand back to the original.
- E, (x − 19)(x − 19): This expands to x² − 38x + 361, which has a x term.
See where this fits: GCSE maths with AQA and Key Stage 3.
Related topics: Expanding brackets, Solving equations, Sequences.
