Home > Subjects > Mathematics > Level 2 > 2.1 Algebra (AS90284) > Subject content > Factorising algebraic expressions
- Subject: Mathematics
- AS: AS90284
- Level: 2
- Credits: 4
- External
Mathematics 2.1 Manipulate algebraic expressions and solve equations
Factorising algebraic expressions
Factorise is the reverse of expand i.e. put in brackets.
To factorise, rewrite the expression as factors multiplied together.
Two terms
Look for the largest number that will divide into all terms and any common letters.
e.g. 12x + 20xy = 4x(3 + 5y)
This is because 4x is the largest factor of both 12x and
20xy.
Check by expanding your answer.
See online examples of common factors.
Two terms: Difference of two squares
Look for two square terms that have been subtracted.
e.g. 4x2 – 9
= (2x)2 – 32
= (2x + 3)(2x – 3)
See online examples of factoring the difference of two squares and practice with factoring difference of two squares.
Three terms
Look for a common factor first and then factorise further.
e.g. 3x2 – 6x – 15 = 3(x2 – 2x – 5)
If no common factor, look for two numbers that multiply to give the number by itself (constant term) and add to give the number in front of x.
e.g. x2 – 2x - 15 = (x + 3)(x – 5)
This is because –5 times 3 = –15 and –5 plus 3 = –2
Check
Hence 3x2 – 6x – 15 = 3(x + 3)(x – 5)
If there is no number written in front of x remember it is really a 1.
e.g. x2 + x – 6 = (x + 3)(x – 2)
This is because 3 times -2 = –6 and 3 plus –2 = 1
See notes on:
Harder factorising
If there is a number in front of x2 that is not a common factor use guess and check or the following method.
Two numbers that multiply to give –6 and add to give +5 are +6 and –1. Write 5x as 6x - x.
e.g. 2x2 + 5x – 3= 2x2 + 6x – x – 3
When there are four terms, factorise in pairs first.
e.g. 2x2 + 6x – x – 3 = 2x(x + 3) – 1(x + 3)
Take out the common bracket (x + 3).
e.g. 2x(x + 3) – 1(x + 3) = (x + 3)(2x – 1)
See notes on:
- Factoring
- Algebasics – Section 8: Factoring (Macromedia Flash® and sound required)
