AQA · Mathematics · 8300
GCSE Maths: Factorisation: splitting the middle
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Factorisation: splitting the middle (Corbettmaths Video 119), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
10 flashcards · Free to study · No account needed
Study this deck
Preparing your cards…
All questions and answers
Read through the full deck, or practise recalling each answer above.
What is the general approach called when factorising a quadratic like 2x² + 7x + 5 by rewriting the middle term?
Show answer
Splitting the middle (term). You find two numbers that multiply to give (first coefficient × constant) and add to give the middle coefficient, then rewrite and group.
When factorising 3x² + ax + 10, how many possible integer values can a take?
Show answer
Multiple values (both positive and negative). The question states a can be positive or negative, requiring all factor pairs of 3 × 10 = 30.
What type of quadratic is x² − 121?
Show answer
Difference of two squares. It factorises as (x − 11)(x + 11) without needing to split the middle.
What is the first step when asked to 'factorise fully' an expression like 2y² − 50?
Show answer
Take out the common factor (here, 2) to get 2(y² − 25), then factorise what remains if possible.
Why is (x + 5)(x + 6) incorrect as the factorisation of x² − 11x + 30?
Show answer
The signs are wrong. (x + 5)(x + 6) expands to x² + 11x + 30, but the middle term should be −11x. The correct factorisation is (x − 5)(x − 6).
How many positive integer values of a make x² + ax + 24 factorisable?
Show answer
8 values. Each factor pair of 24 gives one value of a (the sum of the pair): (1,24)→25, (2,12)→14, (3,8)→11, (4,6)→10, and their reverses give the same sums.
What is the substitution strategy to factorise 10(y − 3)² + 9(y − 3) + 2?
Show answer
First factorise 10x² + 9x + 2, then replace every x in the factorised form with (y − 3).
To factorise ax² + bx + c (a ≠ 1) by splitting the middle, find two numbers that multiply to ? and add to b.
Show answer
a × c
What pattern does the quadratic y² − 9w² follow?
Show answer
Difference of two squares: y² − (3w)². It factorises as (y − 3w)(y + 3w).
How do you factorise (x + 4)² + 3(x + 4) fully?
Show answer
Take out the common factor (x + 4) to get (x + 4)[(x + 4) + 3] = (x + 4)(x + 7).
Want to create your own cards? Create a free account. AI generation uses credits.