Uvero — STEM Learning

Quadratics by Factorisation

A quadratic in zero form can be solved using factors and the zero-product property. Each factor supplies a root only after the product equals zero. At Grade 10, fluent symbolic work must stay connected to graphs, tables, diagrams and real quantities.

Worked reasoning

Factor as $(x-3)(x-4)=0$ .
Set each factor to zero.

Solve $x^2-7x+12=0$ .

$x=3$ or $4$

$x=-3$ or $-4$

$x=2$ or $6$

$x=12$

Which statement best captures the central mathematical idea in Quadratics by Factorisation?

Each factor supplies a root only after the product equals zero.

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

A memorised formula is valid even when its conditions are not met.

The diagram or notation replaces the need to justify each mathematical step.

When starting a problem about Quadratics by Factorisation, which move is most reliable?

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for quadratics by factorisation.

Round every value before identifying the mathematical structure.

Choose the longest available formula and substitute immediately.

Assume the desired conclusion and work backwards without checking equivalence.

Which statement is a misconception that must be rejected when working with Quadratics by Factorisation?

A memorised rule may be used without checking signs, domains, units, graph family or geometric hypotheses.

Each factor supplies a root only after the product equals zero.

Identify the mathematical family, list the given quantities and state the domain or geometric conditions for quadratics by factorisation.

Use substitution, a second representation or a magnitude estimate to verify the result.