Year 9 Interactive Maths - Second Edition

Factorisation of Quadratic Trinomials

The Distributive Law is used in reverse to factorise a quadratic trinomial, as illustrated below.

Consider the expansion of (x + 2)(x + 3).

We notice that:

• 5, the coefficient of x, is the sum of 2 and 3.

• 6, the independent term, is the product of 2 and 3.

Note:

The product of two linear factors yields a quadratic trinomial; and the factors of a quadratic trinomial are linear factors.

Now consider the expansion of (x + a)(x + b).

Coefficient of x = a + b = Sum of a and b.
Independent term = ab = Product of a and b.

In general:

To factorise a quadratic trinomial, find two numbers whose sum is equal to the coefficient of x, and whose product is equal to the independent term.

Example 12

Solution:

Check:

Key Terms

quadratic trinomial, independent term, coefficient, linear factor