1 / 20

Year 9/GCSE: Factorising Quadratics

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.

meadow
Download Presentation

Year 9/GCSE: Factorising Quadratics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Year 9/GCSE: Factorising Quadratics Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 27th August 2013

  2. 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)

  3. Factor Challenge 5 + 10x x – 2xz x2y – xy2 10xyz – 15x2y xyz – 2x2yz2 + x2y2

  4. 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) ? ? ? ? ? ? ? ? ? ? ? ? ?

  5. Factorising out an expression It’s fine to factorise out an entire expression: ? ? ? ?

  6. Harder Factorisation ? ?

  7. 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’.

  8. 2. Expand ? How does this suggest we can factorise say ? ? Is there a good strategy for working out which numbers to use?

  9. 2. A few more examples: ? ? ? ? ?

  10. 2. 1 ? 11 2 ? ? 3 12 ? ? ? 4 ? 13 5 ? ? 6 ? 14 7 ? ? 8 ? 9 ? 10 ? Hardcore ? ? N N ? N ? N ?

  11. 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’.

  12. 3. Difference of two squares Firstly, what is the square root of: ? ? ? ? ?

  13. 3. Difference of two squares Click to Start Bromanimation

  14. 3. Difference of two squares Examples ? ? ? ? ? ? (Strictly speaking, this is not a valid factorisation)

  15. 3. Difference of two squares ? Working in pairs: ? ? ? ? ?

  16. 3. Difference of two squares Exercises: ? 1 ? 2 ? 3 ? 4 ? 5 ? 6 ? 7 ? 8 ? 9 ? 10

  17. 4. ? Factorise using: The ‘commando’ method* b. Splitting the middle term * Not official mathematical terminology.

  18. 4. ? ? ? ?

  19. 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

  20. 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) ? ? ? ? ? ? ? ? ? ?

More Related