Term 2 Week 2

graph of a quadratic equation - very useful for calculating how things fall

This weeks algebra delves more deeply into the mystery of factorising binomials and trinomials.

Last week we covered how to factorise by grouping in pairs.

This week students should be able to recognise quadratic trinomials of the form ax² + bx + c (where a, b and c are numbers)

This week we are continuing to look for ways to factorise expressions.

One strategy is to look for any expressions that match the pattern for 'difference of squares' For example:

a² - 4

we recognise as a 'difference of squares', and so can easily factorise it to:

(a + 2)(a - 2)

However expressions like this are more tricky, and will require a lot more patience and practice:

5k² -12k + 4

To do this one we have to find two numbers that multiply to equal 20 (a times c, or 5 times 4) and also add up to -12 (b). We work out with trial and error that -2 & -10 multiply to equal 20 and add up to -12. Now we can 'split' the middle term and apply the strategy 'group in pairs' that we learned last week.

= 5k² -10k -2k + 4
= 5k(k - 2) -2(k - 2)
=(5k - 2)(k -2)

There, fully factorised! Wasn't that easy! Actually this is one of the most challenging Algebraic things students will do all year. If you are finding this hard you are not alone! Make sure you get one of the maths teachers to help you at lunch or outside of class.

Good luck!

The Products and Factors Assignment 2 is here
(note c9 assignments are now given and due on Wednesdays)
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