Factorising Quadratics – Key Vocabulary

Vocabulary flashcards summarising essential terms and methods for factoring quadratic trinomials as practised in the lecture slides.

Quadratic Expression

An algebraic expression of degree two, generally written in the form ax² + bx + c.

Quadratic Trinomial

A quadratic expression containing three terms: ax² + bx + c.

Monic Quadratic

A quadratic in which the leading coefficient a equals 1 (e.g., x² + bx + c).

Factorising (Factoring)

Rewriting an expression as a product of two or more simpler expressions.

Factor Pair

Two numbers whose product equals a specified constant term (c) in a quadratic trinomial.

Sum-and-Product Method

Factoring technique for monic quadratics that finds two numbers whose sum equals b and whose product equals c.

Trial-and-Error Method

Systematically testing factor pairs until the correct combination that reproduces bx + c is found.

FOIL Method

A mnemonic (First, Outer, Inner, Last) for multiplying two binomials; used in reverse when checking factors.

Prime Quadratic

A quadratic expression that cannot be factorised over the integers.

Difference of Squares

Form a² − b², which factors as (a + b)(a − b).

Perfect Square Trinomial

Trinomial of the form x² ± 2ax + a², which factors as (x ± a)².

Leading Coefficient

The coefficient of x² (the highest-degree term) in a quadratic expression.

Middle Coefficient

The coefficient b of the x term in ax² + bx + c.

Constant Term

The term c in ax² + bx + c that contains no variable.

Zero Product Property

If the product of two factors equals zero, then at least one of the factors must be zero; used to solve quadratic equations after factoring.