Uvero — STEM Learning

Solving by Factorisation

After writing an equation in zero form and factorising, the zero-product property sets each factor equal to zero. A product is zero when at least one factor is zero. A careful solution names the quantities, keeps place value or units visible, and explains why each operation fits.

Worked reasoning

Factor as $(x-3)(x+2)=0$ .
Set each factor to zero.

Solve $x^2-x-6=0$ .

$x=3$ or $x=-2$

$x=2$ or $x=-3$

$x=6$ only

$x=-6$ only

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

A product is zero when at least one factor is zero.

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

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 Solving by Factorisation, which move is most reliable?

Represent the given information clearly and identify the operation or relationship required for solving 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 Solving by Factorisation?

A familiar-looking calculation may be used without checking place value, units, conditions or what the answer represents.

A product is zero when at least one factor is zero.

Represent the given information clearly and identify the operation or relationship required for solving by factorisation.

Estimate first, then reverse the operation or use a second representation to check that the answer is reasonable.