Factorising is like breaking down maths expressions into smaller, simpler... Show more
Mathematics6 views·Updated May 26, 2026·2 pagesMastering Factorisation Techniques
L
Louis Glancy@louisglancy
1
of 2
The Four Types of Factorising
There are four main types of factorising you need to know, and each one has a pattern you can spot. Most expressions with 2 terms use either HCF or DOTS, 3 terms usually need the quadratic method, and 4 terms typically use grouping.
Highest Common Factor (HCF) is your starting point - find the biggest number and letter that appears in all terms. For example, with 3x² + 6x, both terms contain 3x, so you can factor out 3x. It's like reverse multiplication!
The grouping method works brilliantly with 4 terms. You split them into two pairs, factor each pair separately, then spot the common bracket that appears twice. When you see 3ac + 6c + ad + 2d, you get 3c + d, which becomes .
Quick Tip: Always check your factorising by multiplying the brackets back out - you should get your original expression!
2
of 2
Quadratics and DOTS Methods
Quadratic factorising uses trial and error, but there's a system to it. Start with (x )(x ) since you need x² as your first term. Then hunt for two numbers that multiply to give your last term - if it's negative, your signs will be different in the brackets.
Check your work by using FOIL (First, Outer, Inner, Last) to multiply back out. The outer and inner terms should add up to your middle term. Don't worry if your first guess is wrong - just try different number pairs until it works!
DOTS (Difference of Two Squares) is actually the easiest once you spot the pattern. You need something squared minus something else squared, like x² - 36. Just rewrite it as (x)² - (6)², then use the magic formula: .
Remember: With DOTS, you always get one bracket with addition and one with subtraction - it's the same numbers, just different signs!
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Mathematics6 views·Updated May 26, 2026·2 pagesMastering Factorisation Techniques
L
Louis Glancy@louisglancy
Factorising is like breaking down maths expressions into smaller, simpler parts - think of it as finding what pieces multiply together to make the original expression. You'll use these skills constantly in your Junior Cert maths, so mastering these four... Show more
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The Four Types of Factorising
There are four main types of factorising you need to know, and each one has a pattern you can spot. Most expressions with 2 terms use either HCF or DOTS, 3 terms usually need the quadratic method, and 4 terms typically use grouping.
Highest Common Factor (HCF) is your starting point - find the biggest number and letter that appears in all terms. For example, with 3x² + 6x, both terms contain 3x, so you can factor out 3x. It's like reverse multiplication!
The grouping method works brilliantly with 4 terms. You split them into two pairs, factor each pair separately, then spot the common bracket that appears twice. When you see 3ac + 6c + ad + 2d, you get 3c + d, which becomes .
Quick Tip: Always check your factorising by multiplying the brackets back out - you should get your original expression!
2
of 2Sign up to see the content. It's free!
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Quadratics and DOTS Methods
Quadratic factorising uses trial and error, but there's a system to it. Start with (x )(x ) since you need x² as your first term. Then hunt for two numbers that multiply to give your last term - if it's negative, your signs will be different in the brackets.
Check your work by using FOIL (First, Outer, Inner, Last) to multiply back out. The outer and inner terms should add up to your middle term. Don't worry if your first guess is wrong - just try different number pairs until it works!
DOTS (Difference of Two Squares) is actually the easiest once you spot the pattern. You need something squared minus something else squared, like x² - 36. Just rewrite it as (x)² - (6)², then use the magic formula: .
Remember: With DOTS, you always get one bracket with addition and one with subtraction - it's the same numbers, just different signs!
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You can download the app in the Google Play Store and in the Apple App Store.
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