Factorising Quadratic Trinomials

A quadratic trinomial has three terms and the highest power is usually $x^{2}$.

Factorising a quadratic trinomial writes it as a product of two brackets.

This method is important for solving quadratic equations and simplifying algebra.

A trinomial has three terms. A quadratic trinomial has degree 2.

For $x^{2} + b$$x + c$, find two numbers whose product is c and whose sum is b.

For a$x^{2} + b$$x + c$, split the middle term using two numbers whose product is ac and whose sum is b.

After splitting, factorise by grouping.

Expansion is the best way to check the answer.

You will learn

• Recognise quadratic trinomials.
• Factorise $x^{2} + b$$x + c$.
• Use spli$t-m$iddl$e-t$erm method.
• Factorise a$x^{2} + b$$x + c$ when a is not 1.
• Check factors by expansion.