![]() Learners could try solving x2 + 17x + 30 = 0 and 2x2 + 17x + 30 = 0 to see if they can do them themselves. There are other perfectly good ways of factorising non-monic quadratics, but this is a method learners (or even teachers) may not have seen. Sometimes learners do this by trial and error, but a more systematic method is to place x’s in two brackets and write the coefficient of x (which is 2, here) three times: You can still solve it by factorising, but the factorising is harder now because the lefthand side is non-monic (i.e., the coefficient of x2 is not 1). Q: What if I change the starting equation by sticking a ‘2’ on the front: So in this case, either x + 3 = 0 or x – 10 = 0, giving the two answers x = –3 or 10. Now if two numbers multiply to make zero, either the first one is zero or the second one is zero. (The 3 and the –10 come from the fact that their sum is –7, the coefficient of x, and their product is –30, the constant term.) The easiest way is to factorise the left-hand side Starter activity Q: Do you remember how to solve a quadratic equation like: Lots of practice happens along the way, while something a bit more interesting is going on. How can KS4 learners become confident and fluent with techniques such as factorising quadratics without simply ploughing through pages of exercises? One way is to offer a scenario in which they need to construct their own quadratic equations in order to solve a bigger problem. Practise solving quadratic equations by factorising while working on a deeper problem ![]() When learners are bored in maths lessons they sometimes ask, “When will we ever actually use this?” But even topics that are unlikely to feature in everyday life can still be fun for learners to work on if they experience them as a puzzle to solve, says Colin Foster… When learners are bored in maths lessons they sometimes ask, “When will we ever actually use this?” But even topics that are unlikely to feature in everyday life can still be fun for learners to… ![]()
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