Name:
CAPS Reference
Topic
Gr 10
Date: Term 1
Time: 1 HR
Factorising
Highest Common Factor (HCF) and trinomial
factorising
1. GOT IT! [15 MIN]
Highest Common Factor …
….is the biggest common factor of two or more expressions.
General Factorising
Example 1: Factorise the following.
4𝑥𝑥 2 − 𝑥𝑥
If you expand it, it will look as follow:
= 4 × 𝑥𝑥 × 𝑥𝑥 − 𝑥𝑥
= 𝑥𝑥(4𝑥𝑥 − 1)
Test!!!
= 𝑥𝑥(4𝑥𝑥 − 1)
= 4𝑥𝑥 2 − 𝑥𝑥
You can always test
your answer to make
sure it is correct.
The HCF in this case is 𝑥𝑥.
1. Look at what both terms have similar.
2. Take out the HCF
3. Put the HCF in front and the rest of the
terms goes in a new bracket.
Example 2: 9𝑎𝑎3 − 3𝑎𝑎2
= 9 × 𝑎𝑎 × 𝑎𝑎 × 𝑎𝑎 − 3 × 𝑎𝑎 × 𝑎𝑎
BUT!!!
= 3𝑎𝑎2 (3𝑎𝑎 − 1)
∴ 3 is also similar
9=3×3
Remember!!!
Mainly when you have to factorise, it means that when you multiply numbers/exponents it
creates an expression.
Trinomial factorising.
Example: Factorise the following.
𝑥𝑥 2 + 3𝑥𝑥 − 10
Factors of 𝑥𝑥 2 is:
= (𝑥𝑥 − 2)(𝑥𝑥 + 5)
= 𝑥𝑥 × 𝑥𝑥
How do you decide what factors of 10 you should use?
You look at the middle
Factors of 10 is.
−10 = 5 × −2
Take note, that
there are other
factors of 10.
term.
𝑥𝑥
𝑥𝑥
−2
−5
= −2𝑥𝑥 + 5𝑥𝑥
= 3𝑥𝑥
2. GO AHEAD [30 MIN]
Factorise the following:
2.1 4𝑥𝑥 2 + 8
2.2 𝑎𝑎𝑏𝑏 2 − 𝑎𝑎𝑎𝑎
2.5 𝑥𝑥 2 + 𝑥𝑥 − 20
2.6 𝑥𝑥 2 + 15𝑥𝑥 + 56
2.3 9𝑎𝑎𝑎𝑎 − 3𝑎𝑎
2.7 𝑎𝑎2 − 3𝑎𝑎 − 4
2.9 𝑥𝑥 2 − 5𝑥𝑥 + 6
2.11 𝑥𝑥 2 + 7𝑥𝑥 + 12
2.13 𝑥𝑥 2 + 𝑥𝑥𝑥𝑥 − 2𝑦𝑦 2
2.15 2𝑥𝑥 2 + 3𝑥𝑥 − 5
2.4 𝑥𝑥 2 − 12𝑥𝑥 − 28
2.8 𝑎𝑎2 − 5𝑎𝑎 − 14
2.10 𝑎𝑎2 + 4𝑎𝑎 + 3
2.12 3𝑥𝑥 2 + 2𝑥𝑥 − 1
2.14 4𝑎𝑎2 − 14𝑎𝑎 + 6
2.16 3𝑎𝑎2 + 20𝑎𝑎𝑎𝑎 − 7𝑏𝑏 2
3. CHECK YOUR WORK! [15 MIN]
4. HELPFUL VIDEO
https://www.youtube.com/watch?v=JPYfGMeqzzk&list=PLA9E4E2E94F98266E&index=45
https://www.youtube.com/watch?v=q6_pWifXKcQ&list=PLA9E4E2E94F98266E&index=47
https://www.youtube.com/watch?v=S3GNmhI0-sU&list=PLA9E4E2E94F98266E&index=48
https://www.youtube.com/watch?v=87W31FAS8Ig&list=PLA9E4E2E94F98266E&index=77