Factor pair
Find the pair that multiplies to the constant and adds to the coefficient of x.
AQA 8300 · A18 · Quadratic factorisation
Quadratics: both roots, including the one that is zero
The second root. The zero-product step awards both values, and an answer giving one of them is a half-answer no matter how clean the factorisation was.
Reviewed family · Studara-authored items · No grade-uplift claim
The lost mark
One answer. Several places the method can fail.
Studara does not reduce the response to right or wrong. The reviewed contract checks these states independently.
Factorised form
Write the expression as a product of two brackets equal to zero.
Both roots
Set each bracket to zero separately and state both solutions.
Why it goes wrong
The diagnosis stays uncertainty-safe.
A wrong response can support a specific measured diagnosis. A blind multiple-choice diagnostic records only a possible cause until later working provides stronger evidence.
01
The error
Stopping at the factorised form, or solving x(x − 5) = 0 as x = 5 — discarding the root that comes from the bracket that is just x.
02
Why it survives revision
One root is correct, so the answer earns partial credit and feels finished. A root of 0 also does not look like a solution: it reads as “nothing” rather than as a value, so it is dropped without a decision being made.
The worked repair
Repair the smallest broken step.
Teaching is not evidence. This one move is the repair; the proof checks begin after it disappears.
Write both brackets set to zero as two separate equations, on two separate lines, before solving either.
What happens after the repair
Correction is the start, not the result.
Immediate
Asked again straight away, on a different question
The repair leaves the screen and a new authored item checks the method unassisted. Being taught something is never evidence that it was learned, so this is the first stage that counts at all.
Delayed
Asked again after at least 1 day
A parallel form of the same method, unassisted, with the repair no longer on screen. A retest in the same session does not count.
Transfer
Asked again when the surface changes
The transfer form uses a non-monic quadratic, or asks where the curve crosses the x-axis — the same roots, asked for in a form that does not cue “factorise”.
Exam
Asked again under exam conditions
Timed, carrying the mark tariff, in an exam-like response format and aligned to the specification. Any one of those missing and the evidence is refused.
REVIEWED BOUNDARY
This page covers one reviewed family: A18 · Quadratic factorisation. Factor pair, zero-product rule and both roots. Other families within the same GCSE Maths topic are outside this reviewed journey, and Studara does not apply the proof label to material that has not been reviewed. No grade-uplift claim is made anywhere on this site.
Straight answers
Before you use this guide.
Why does my quadratic have two answers?
Because a product is zero when either factor is zero. Each bracket gives one solution, so a factorised quadratic has two roots unless the brackets are identical.
What if one of the roots is 0?
It is still a root and still earns the mark. x(x − 5) = 0 has solutions x = 0 and x = 5 — zero is a value, not the absence of one.
Does Studara guarantee a higher grade?
No. Studara has not run a controlled outcome study and publishes no grade-uplift claim. What has been measured, what is withheld, and the metric that failed its bar are all on the public evidence page.
Turn this method into evidence