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Year 9/GCSE: Factorising Quadratics. Dr J Frost (jfrost@tiffin.kingston.sch.uk) . Last modified: 27 th August 2013. Factorising Overview. Factorising means : To turn an expression into a product of factors. So what factors can we see here?. Year 8 Factorisation. Factorise.
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Year 9/GCSE: Factorising Quadratics Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 27th August 2013
Factorising Overview Factorising means : To turn an expression into a product of factors. So what factors can we see here? Year 8 Factorisation Factorise 2x2 + 4xz 2x(x+2z) Year 9 Factorisation Factorise x2 + 3x + 2 (x+1)(x+2) A Level Factorisation Factorise 2x3 + 3x2 – 11x – 6 (2x+1)(x-2)(x+3)
Factor Challenge 5 + 10x x – 2xz x2y – xy2 10xyz – 15x2y xyz – 2x2yz2 + x2y2
Revision Extension Question: What integer (whole number) solutions are there to the equation Answer: . So the two expressions we’re multiplying can be This gives solutions of 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) ? ? ? ? ? ? ? ? ? ? ? ? ?
Factorising out an expression It’s fine to factorise out an entire expression: ? ? ? ?
Four different types of factorisation 1. Factoring out a single term 2. ? ? 4. 3. Difference of two squares ? ? Strategy: either split the middle term, or ‘go commando’.
2. Expand ? How does this suggest we can factorise say ? ? Is there a good strategy for working out which numbers to use?
2. A few more examples: ? ? ? ? ?
2. 1 ? 11 2 ? ? 3 12 ? ? ? 4 ? 13 5 ? ? 6 ? 14 7 ? ? 8 ? 9 ? 10 ? Hardcore ? ? N N ? N ? N ?
Four different types of factorisation 1. Factoring out a term 2. ? ? 4. 3. Difference of two squares ? ? Strategy: either split the middle term, or ‘go commando’.
3. Difference of two squares Firstly, what is the square root of: ? ? ? ? ?
3. Difference of two squares Click to Start Bromanimation
3. Difference of two squares Examples ? ? ? ? ? ? (Strictly speaking, this is not a valid factorisation)
3. Difference of two squares ? Working in pairs: ? ? ? ? ?
3. Difference of two squares Exercises: ? 1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 ? 8 ? 9 ? 10
4. ? Factorise using: The ‘commando’ method* b. Splitting the middle term * Not official mathematical terminology.
4. ? ? ? ?
Exercises ? 1 ? 2 ? 3 4 ? 5 ? ‘Commando’ starts to become difficult from this question onwards. 6 ? ? 7 ? 8 ? 9 ? 10 11 ? Well Hardcore: ? N ? N
Summary For the following expressions, identify which of the following factorisation techniques that we use, out of: (it may be multiple!) 1 Factorising out single term: 2 Simple quadratic factorisation: 3 Difference Of Two Squares: 4 Commando/Splitting Middle Term: 5 Pairwise: 6 Intelligent Guesswork: (1) (3) (1), (3) (2) (4) (2), (6) (5) (1), (2) (5) or (6) (1), (3) ? ? ? ? ? ? ? ? ? ?