Sheet № 85 · Foundation + Higher · AQA · Edexcel · OCR
Factorising Quadratics –
Factorising quadratics reverses the process of expanding double brackets. It is one of the most commonly tested algebra skills at GCSE and a prerequisite for solving quadratic equations, simplifying algebraic fractions, and sketching parabolas.
§Key definitions
Question:
Factorise x² + 9x + 20.
Answer:
(x + 4)(x + 5)
Q1 (Foundation):
Factorise x² + 7x + 12.
Q2 (Foundation):
Factorise x² - 2x - 15.
Q3 (Higher):
Factorise x² - 10x + 25.
§Formulas to memorise
x² + bx + c = (x + p)(x + q) where p + q = b and pq = c
Check: (x + p)(x + q) = x² + (p + q)x + pq
Find the pair whose sum equals b.
b = -11 and c = 24. Both numbers must be negative (negative sum, positive product).
Worked example
Factorise x² + 9x + 20.
Working:
⚠ Common mistakes
- ✗Getting signs wrong when c is negative. If c < 0, one factor must be positive and one negative. List pairs systematically to avoid missing the correct combination.
- ✗Choosing factors that multiply correctly but do not add correctly. Always check both conditions: the pair must multiply to c and add to b.
- ✗Forgetting to check by expanding. A quick expansion confirms your answer and prevents dropped marks. It takes only a few seconds.
✦ Exam tips
- →Write out all factor pairs neatly before choosing. This avoids guesswork and shows the examiner your method.
- →If both b and c are positive, both numbers in the brackets are positive. If b is negative and c is positive, both numbers are negative.
- →When a question says "factorise and hence solve," factorise first, then set each bracket equal to zero.