1 / 21

Factorising

Learn 5 methods of factorising in this PowerPoint tutorial, including creating brackets and solving quadratic trinomials. Understand common factors, difference of two squares, grouping, and easy quadratic trinomials with step-by-step examples.

ktina
Download Presentation

Factorising

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. Factorising Creating brackets

  2. In this powerpoint, we meet 5 different methods of factorising. This involves taking a term outside the brackets. Always try to do this first. Type 1 – Common Factor Type 2 – Difference of Two Squares Try this when you have two terms with a minus between Type 3 – Grouping This is the easiest one to pick – use it when there are 4 terms!

  3. Use these for expressions with 3 terms. They will be of the format x2 + bx + c (Type 4) OR ax2 + bx + c (Type 5) Types 4 and 5 Quadratic trinomials Where a, b and c are just numbers Factorising just makes me sooooo happy!!

  4. Summary

  5. Always look for a common factor! Type 1 of 5 – common factor Always try this first, regardless of what type it is 3a – 12 = 3(a – 4) 3a2 – 12a = 3a(a – 4) 4b(5a – 3b) 20ab – 12b2 = 30a6 – 15a5 = 15a5(2a – 1) 3a2 + 6a + 12 = 3(a2 + 2a + 4) Remember – take out the largest factor you can!

  6. Type 2 of 5 – diff of 2 squares To qualify as a Type 2, an expression • must have only 2 terms which are SQUARES • must have a MINUS sign separating them Examples a2 – 9 = (a – 3)(a + 3) 16 – a2 = (4 – a)(4 + a) (2b)2– (3a)2 = (2b – 3a)(2b + 3a) 9b2– 25 = (3b – 5)(3b + 5)

  7. LookMum ! It’s a difference of 2 squares! Combining Types 1 and 2 Example 1 .....Factorise 5x2 – 45 STEP 1 Treat as a Type 1, and take out common factor first, 5 Write 5(x2 – 9) STEP 2 Now do expression in brackets as a Type 2 Write 5(x – 3)(x + 3)...ANS!

  8. Now check out the thing in each bracket. We can factorise the first one, but not the second. Y’can’t factorise a SUM of two squares Stupid! x2 + 9 has to stay as it is. It’s not the same as (x + 3)(x + 3) is it now??? Example 2 .....Factorise x4 – 81 STEP 1 Treat as a Type 2, and write as difference of 2 squares..... (x2 – 9)(x2 + 9) STEP 2 (x2 – 9)(x2 + 9) (x – 3)(x + 3)(x2 + 9)....ANS!!

  9. Example 3 .....Factorise 80a4 – 405b12 STEP 1 Identify common factor, 5 and remove Write 5(16a4 – 81b12) STEP 2 Now work on the terms in the brackets This is a difference of 2 squares and becomes (4a2 – 9b6) (4a2 + 9b6) Write 5(4a2 – 9b6) (4a2 + 9b6) STEP 3 Now work on the terms in the 1st bracket. This is a difference of 2 squares and becomes (2a – 3b3) (2a + 3b3) . Write 5(2a – 3b3) (2a + 3b3) (4a2 + 9b6)

  10. Example 4 .....Factorise 9a2 – (x – 2a)2 Just treat as difference of 2 squares of the format 9a2 – b2 where the b = [x – 2a] Factorising it then becomes = (3a – b)(3a + b) And then replacing the b with [x – 2a] we get = (3a – [x – 2a])(3a + [x – 2a]) Now get rid of square brackets = (3a – x + 2a)(3a + x – 2a) Clean up = (5a – x )(a + x) Ans!! You could check your answer by expanding it and also expanding the original question. They should both give the same thing.

  11. No need to be confused! Type 3 of 5 – Grouping You can tell when you’ve got one of these because there are FOUR TERMS !!! Example 1 Factorise 2a – 4b + ax – 2bx STEP 1 – split it into “2 by 2” = 2a – 4b + ax – 2bx STEP 2 – factorise each pair separately as Type 1 = 2(a – 2b) +x(a – 2b) STEP 3 – take out the (a – 2b) as a common factor = (a – 2b)(2 + x)...ans!!

  12. If these are the same, it’s a good sign! Type 3 of 5 – Grouping Example 2 Factorise xy + 5x – 2y – 10 STEP 1 – split it into “2 by 2” = xy + 5x – 2y – 10 STEP 2 – factorise each pair separately as Type 1 = x(y + 5) – 2 (y +5) STEP 3 – take out the (y + 5) as a factor = (y + 5)(x – 2) ans!!

  13. Ewbewdy!! They’re the same! On my way to a VHA   Type 3 of 5 – Grouping Example 3 Factorise x2 – x – 5x + 5 STEP 1 – split it into “2 by 2” = x2 – x – 5x + 5 STEP 2 – factorise each pair separately as Type 1 = x(x – 1) – 5 (x – 1) STEP 3 – take out the (x – 1) as a factor = (x – 1 )(x – 5) ans!!

  14. Awwright! They’re the same!! Example 4 - harder Factorise x2 – 4y2 – 2ax – 4ay STEP 1 – split it into “2 by 2” = x2 – 4y2 – 2ax – 4ay STEP 2 – factorise each pair separately 1st pair – Type 2 2nd pair – Type 1 = (x – 2y) (x + 2y) – 2a (x + 2y) STEP 3 – take out the (x + 2y) as a factor = (x + 2y)(x – 2y – 2a) ans!!

  15. Type 4 of 5 – Easy Quadratic Trinomial You can usually pick these as they have 3 TERMS Example 1 .....Factorise x2 + 5x + 6 STEP 1 – Make 2 brackets (x..............)(x.............) STEP 2 – Look for 2 numbers that Add to make +5 +2 & +3 Multiply to make +6 STEP 3 – Put ‘em in the brackets (x + 2)(x + 3)

  16. Type 4 of 5 – Easy Quadratic Trinomial Example 2 .....Factorise 2x2 – 6x – 20 STEP 1 – take out a common factor (remember this should be your 1st step EVERY time!!) = 2(x2 – 3x – 10) STEP 2 – Ignore the 2. For the expression inside the brackets, look for 2 numbers that Add to make – 3 +2 & – 5 Multiply to make – 10 STEP 3 – Put ‘em in the brackets 2(x + 2)(x – 5)

  17. Type 4 of 5 – Easy Quadratic Trinomial Example 3 .....Factorise 6 + 5x – x2 STEP 1 – Rearrange into “normal” format with x2 at the front, then x, then the number = – x2 + 5x + 6 STEP 2 – Now take out a common factor – 1 = – (x2 – 5x – 6) STEP 3 – Ignore the minus. Look for 2 numbers that add to – 5, and multiply to – 6. These are +1 and –6. – (x + 1)(x – 6)

  18. 2 × – 3 = – 6 Type 5 of 5 – Harder Quadratic Trinomial With a number in front of the x2 Example 1 .....Factorise 2x2 + 5x – 3 STEP 1 – Draw up a fraction like this STEP 2 – Look for two numbers that ADD to make +5 MULT to make – 6 Numbers are +6, – 1 Note the 2 in bottom must cancel one whole bracket FULLY! So (2x + 6) becomes (x + 3) = (x + 3)(2x – 1) ANS

  19. 3 × – 3 = – 9 Type 5 of 5 – Harder Quadratic Trinomial With a number in front of the x2 Example 2 .....Factorise 3x2 + 8x – 3 STEP 1 – Draw up a fraction like this STEP 2 – Look for two numbers that ADD to make +8 MULT to make – 9 Numbers are +9, – 1 Note the 3 in bottom must cancel one whole bracket FULLY! So (3x + 9) becomes (x + 3) = (x + 3)(3x – 1) ANS

  20. 6 × 10 = 60 Type 5 of 5 – Harder Quadratic Trinomial With a number in front of the x2 Example 3 .....Factorise 6x2 – 19x + 10 STEP 1 – Draw up a fraction like this STEP 2 – Look for two numbers that ADD to make –19 MULT to make 60 Numbers are –4 , –15 Note the 6 in bottom would not cancel either bracket FULLY! So we broke the 6 into 2 x 3 then cancelled. = (3x – 2)(2x – 5) ANS

  21. Now wozn’t that just a barrel of fun??

More Related