Factors of Quadratic Expressions — O/L Mathematics

What must I remember about Factors of Quadratic Expressions?

• Quadratic trinomials take standard algebraic form: ax² + bx + c, where a, b, and c are real constants and a ≠ 0.
• Factorising monic quadratics (a = 1): Find two integers p and q such that their sum equals b (p + q = b) and their product equals c (pq = c); expression factors as (x + p)(x + q).
• Factorising non-monic quadratics (a ≠ 1): Find two numbers whose product is ac and sum is b; split the middle term bx into two terms and factorise by grouping pairs.
• Difference of two squares identity: a² - b² = (a - b)(a + b); useful for both variable expressions and numerical evaluation.
• Common factor extraction rule: Always inspect all terms for a common numerical or algebraic factor and extract it before attempting quadratic factorisation.

Test yourself (1 minute)

1. Sign errors in middle-term splitting

   If c is positive, both p and q share the sign of b; if c is negative, p and q have opposite signs, with the larger magnitude matching the sign of b.

2. Incomplete factorisation penalty

   Expressions like 2x² - 8 must be factored completely as 2(x² - 4) = 2(x - 2)(x + 2); leaving 2(x² - 4) forfeits full marks.

3. Negative leading coefficient

   When factoring -x² + bx + c, extract -1 first: -(x² - bx - c).

Practise Factors of Quadratic Expressions questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 7)

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Where does Factors of Quadratic Expressions fit in the syllabus?

Grade 10 · Term 1