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Factorising Harder Quadratics

Factorising Harder Quadratics. Slideshow 16 Mathematics Mr Sasaki Room 307. Objectives. Factorise quadratics in the form where and are divisible by . Factorise other quadratics in the form . Factorising Quadratics - Easy.

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Factorising Harder Quadratics

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  1. Factorising Harder Quadratics Slideshow 16 Mathematics Mr SasakiRoom 307

  2. Objectives • Factorise quadratics in the form where and are divisible by . • Factorise other quadratics in the form

  3. Factorising Quadratics - Easy We can use methods we already know to solve some quadratics in the form . Example Solve . If we can divide all terms by the coefficient, we can remove it and factorise the quadratic in the form .

  4. Factorising Quadratics - Easy

  5. Factorising Quadratics - Typical As you should know, we were lucky with the questions on the last worksheet. Usually it’s more complicated. Let’s think back to expressions in the form . What are our two simultaneous equations for the numbers and ? We also use this idea for quadratics in the form .

  6. Factorising Quadratics - Typical For a quadratic in the form , we need to consider two numbers. Example (Or vice-versa.) Factorise. We can write the coefficient of (1) as the sum of . Finally, we group the first two and last two terms.

  7. Factorising Quadratics - Typical Example Let’s try one more example. Factorise. (Or vice-versa.)

  8. Factorising Quadratics - Easy

  9. Factorising Quadratics - Medium

  10. Factorising Quadratics - Hard

  11. Squaring and Square Rooting- Drill Let’s have a bit of practice!

  12. Factorising Quadratics - Challenging Some of those quadratics are tough to factorise because big numbers have a lot of factors… For a difficult quadratic, it may be more sensible to pretend its equal to zero, solve it and then factorise the expression. If a quadratic equation has solutions or , how does it factorise? , we learned this from Grade 8 last year!

  13. Factorising Quadratics - Challenging For Do you remember the formula for solving a quadratic equation? Let’s try factorising using this with an easy example. Example Factorise . First, let . Now… We get . So how does our expression factorise?

  14. Factorising Quadratics - Challenging Example Now some of those quadratics on the hard sheet especially were tough. Let’s try again. Factorise . First, let. ( We get . So we have… This is factorised. No! Is this correct? We need to multiply it by 15.

  15. Factorising Quadratics - Challenging In fact, when we solve and get two solutions and …we substitute these into… So, as , and , we get… And that’s it! It is a long process but it’s easier with big numbers, especially when is a big product! Let’s try some questions using this method.

  16. Factorising Quadratics - Regular

  17. Factorising Quadratics - Applied (any order) mm

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