Common sign errors in factorisation
These are mistakes where students choose the wrong signs in the factors while factorising a quadratic equation.
Practice This ConceptMain explanation
Teacher explanation
Sign errors happen because students often match only the product and forget how the middle term controls the signs. Correct factorisation must satisfy both the constant term and the middle term.
Example
x^2 - 8x + 15 = (x - 3)(x - 5), not (x + 3)(x + 5).
Simple analogy
Product fixes the pair, middle term fixes the signs.
Common confusion
Students may use two positive factors even when the middle term is negative.
Exam tip
For a positive constant with a negative middle term, both signs inside the brackets are usually negative.
Answer writing and exam use
1-mark use
Write the exact meaning of common sign errors in factorisation in one clean line.
2-mark use
Define common sign errors in factorisation and add one example or condition.
3-mark use
Explain common sign errors in factorisation, show the method or example, and mention the common mistake.
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