Quadratic Functions and Equations in One Variable · 1.1.6
Solving by factorisation
Students rearrange the quadratic equation into the form ax² + bx + c = 0, factorise the left side into two linear factors, then apply the fact that if the product of two factors is zero, at least one factor must be zero, to find the roots.
The official learning standard (1.1.6)
“Determine the roots of a quadratic equation by the factorisation method.”
What it means
Students rearrange the quadratic equation into the form ax² + bx + c = 0, factorise the left side into two linear factors, then apply the fact that if the product of two factors is zero, at least one factor must be zero, to find the roots.
How it is examined
Factorisation is one of the most frequently tested skills in both papers: Paper 1 includes direct objective questions solving simple quadratic equations, while Paper 2 often embeds it within multi-step problems, such as those formed from word situations or simultaneous equations.
Worked example
Solve the quadratic equation x² + 2x − 15 = 0 by factorisation.
- Find two numbers that multiply to −15 and add to 2: 5 and −3.
- Factorise: x² + 2x − 15 = (x + 5)(x − 3) = 0.
- By the zero product property, x + 5 = 0 or x − 3 = 0.
- Solve each: x = −5 or x = 3.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What is the first step when solving by factorisation?
First rearrange the equation so that one side equals zero, giving the standard form ax² + bx + c = 0. Only after this can the expression be factorised correctly and the zero product property applied.
What if the quadratic doesn't factorise nicely?
This standard focuses on equations that factorise into whole-number or simple fraction factors. If trial pairs of factors of a and c do not work after a reasonable check, the equation likely needs a different method, such as completing the square or the quadratic formula.
Why do we set each factor to zero?
This uses the zero product property: if two numbers multiply to give zero, at least one of them must be zero. Since (x + p)(x + q) = 0 means the product of the two factors is zero, at least one factor, x + p or x + q, must equal zero.