MATHEMATICS From 3 Factorization of

Introduction Objectives: Encouraged to practice thinking skills such as ‘trial and error’ or ‘use equations’. Target: After the lesson, students should be able to do simple factorization. Duration: 30 mins.

Introduction Target group: Form 3 students. Assumption: Students are expected to know how to solve simple linear equations.

What shall we get when we expand ?

What shall we get when we expand ? + qx

What shall we get when we expand ? + qx + px

What shall we get when we expand ? + qx + px + pq

What shall we get when we expand ? Simplify by taking the x out. + qx + px + pq

What shall we get when we expand ? Answer : + (p + q) x + pq

Consider this example Expand : (x + 2)( x + 3)

Consider this example Expand : (x + 2)( x + 3) + 3x

Consider this example Expand : (x + 2)( x + 3) + 3x + 2x

Consider this example Expand : (x + 2)( x + 3) + 3x + 2x + 2x3

Consider this example Expand : (x + 2)( x + 3) + 3x + 2x + 2x3 Again, simplify by taking the x out. + 3x + 2x + 2x3

Consider this example Expand : (x + 2)( x + 3) + (2 + 3) x + 2x3 Therefore the answer is + (2 + 3) x + 2x3

(x + 2)( x + 3) + (2 + 3) x + 2x3 = + (p + q) x + pq = Compare with the previous example + (2 + 3) x + 2x3 = (x + 2)( x + 3) + (p + q) x + pq =

EASY!! Now, what are the answers for the following expression ? (x+4)(x+7) = x2+ ( ? )x + ( ? ) The answer is EASY!! (x+4)(x+7) = x2+ ( )x + ( ) 11 28 4x7 4+7

To do it the other way round is harder. Can you do this? = (x + ? ) (x + ? ) The answer is = (x + ) (x + ) 2 5 2 x 5 2 + 5

Steps to factorize : = (x + ? ) (x + ? ) Fist draw two brackets

Then consider the factors of 10 Steps to factorize : = (x + ? ) (x + ? ) Then consider the factors of 10 That is : 1 x 10 or 2 x 5

WRONG = (x + ? ) (x + ? ) = (x + ) (x + ) 1 Steps to factorize : Try 1 and 10 = (x + ) (x + ) 1 10 WRONG 1+10 is not equal to 7 therefore this is...

CORRECT = (x + ? ) (x + ? ) Try 2 and 5 = (x + ) (x + ) 2 Steps to factorize : = (x + ? ) (x + ? ) Try 2 and 5 = (x + ) (x + ) 2 5 2+5 is equal to 7 therefore this is... CORRECT

Interesting web-sites containing materials of factorization. http://mathforum.com/mathworld/ http://www.crosswinds.net/~despot/felecia/default_html/index.html http://www.algebrahelp.com/

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