Algebra > Quadratics > Solving Quadratics by Factorising
Solving quadratics by factorising helps students connect algebraic structure with the zero product property. The generator now uses selectable worked examples, structured exam-style parts and clearer refresh/replace metadata for review.
Key ideas
Students need to rearrange into the form ax² + bx + c = 0 before solving.
Once a quadratic is factorised, each bracket can be set equal to zero.
The solutions are the x-values that make the whole expression equal zero.
Checking by substitution helps students see whether both solutions work.
Difference of two squares is best introduced after the main factorise-then-solve routine is secure.
Common mistakes
Factorising correctly but forgetting to solve the bracket equations.
Only giving one solution when two are expected.
Trying to factorise before the equation is equal to zero.
Changing signs incorrectly when solving x + a = 0.
Teaching notes
Keep asking: what has to be true for a product to equal zero?
Include equations that need rearranging so students do not learn a narrow routine.
Use graphs later to connect roots with x-intercepts.
Starter ideas
If ab = 0, what can you say about a or b?
Solve x + 7 = 0 and x - 4 = 0.
What is wrong with solving x² + 5x + 6 = 12 by immediately factorising the left-hand side?
Worksheet generation
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