Term 2 Week 3

A very large parabolic mirror used to concentrate the sun's energy - the optimal shape of the mirror is defined by a quadratic equation.

Greetings Al Jabr Lovers!

The Test for the topic Products and Factors is set for Wed week 4 ( 16/05/07)

Make sure to review the text and do as many examples as you can bear. They will get easier.

This Algebra topic is probably the most challenging maths topic that you will do this year. It lays a very good foundation for advanced maths in class 9, 10 and beyond.

This week we are covering the strategies to choose when factorising different types of expressions.

Based on the number of terms in the expression we can choose what to do:
If 2 terms (eg x² - 9) take out any common factors, and check to see if it is a difference of squares.

x² - 9 // yes this is a 'difference of squares'
= (x - 3)(x + 3)

If 4 terms (eg ab + ac + db + dc) take out any common factors, and then group in pairs, and factorise.

ab + ac + db + dc
= (ab + ac) + (db + dc) //this is the 'group in pairs' step
= a(b + c) + d(b + c) //this is the first factorise step - do each pair seperately
= (a + d)(b + c) // finally factorise the whole thing

If 3 terms (eg x² + 5x + 4) take out any common factors, and then use the 'ac' and 'b' values to work out how to split the 'b' term. (a is the coeficient of the x squared part, b is the coeficient of the x term, and c is the constant part at the end) When two values are found that multiply to equal ac and also add to equal b then these values are used to 'split' the b term. The new expression can then be grouped in pairs as per the 4 term expression above. In this example the values 1,4 are the correct ones: 1 x 4 = 4 = ac, and 1 + 4 = 5 = b.

x² + 5x + 4
= x² + 1x + 4x + 4 // split the 'b' term with the values found by using 'ac' and 'b'
= x(x + 1) + 4(x + 1) // group in pairs and factorise
= (x + 4)(x + 1) // finally fully factorise

This stuff is NOT for the faint of heart - but you will become a way better mathemetician and logical thinker if you persevere.

The Johnny Bushelle group is doing a test on Exploring Numbers this Thursday.

The Products and Factors Assignment 3 is here
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