Everything Maths Grade 10

General procedure for factorising a trinomial EMAN

1.Take out any common factor in the coefficients of the terms of the expression to obtain an expression of

the formax^2 +bx+cwherea,bandchave no common factors andais positive.

2.Write down two brackets with anxin each bracket and space for the remaining terms:(x ) (x )

3.Write down a set of factors foraandc.

4.Write down a set of options for the possible factors for the quadratic using the factors ofaandc.

5.Expand all options to see which one gives you the correct middle termbx.

IMPORTANT!

Ifcis positive, then the factors ofcmust be either both positive or both negative. Ifcis negative, it means only
one of the factors ofcis negative, the other one being positive. Once you get an answer, always multiply out
your brackets again just to make sure it really works.

VISIT:

The following video summarises how to factorise expressions and shows some examples.

See video:2DKXatwww.everythingmaths.co.za

Worked example 13: Factorising a quadratic trinomial

QUESTION

Factorise: 3 x^2 + 2x 1.

SOLUTION

Step 1: Check that the quadratic is in required formax^2 +bx+c

Step 2: Write down a set of factors foraandc

(x ) (x )

The possible factors foraare: 1 and 3

The possible factors forcare: 1 and 1

Write down a set of options for the possible factors of the quadratic using the factors ofaandc. Therefore,

there are two possible options.

Option 1 Option 2

(x1) (3x+ 1) (x+ 1) (3x1)

3 x^2  2 x 1 3 x^2 + 2x 1

Step 3: Check that the solution is correct by multiplying the factors

(x+ 1) (3x1) = 3x^2 x+ 3x 1

= 3x^2 + 2x 1

Step 4: Write the final answer

3 x^2 + 2x1 = (x+ 1) (3x1)

26 1.7. Factorisation