Friday, 5 December 2008

Interesting Facts of Factorisation in Quadratic Equation Solving

Why do you learn factorisation?

What is the importance of factorisation?

You may have these questions when you are taught this.

Factorisation is the making of an expression into the product form, that is, (....)(....)(....).

Factorisation ends with all terms in a math expression being connected with parentheses.

What for?

To solve an equation, say, a quadratic equation, you normally make the expression equal to zero.

There is a meaning to this "equal to zero".

Using factoring method, (....)(....) = 0, implies that either one of the (..) can be zero.

Click this link for an explanation to the above statement.

This is will not be so when the terms are in the form A + B = 0 (sum format).

Factorising causes a quick, simple solving of quadratic equation by having the product form to the expression.

Example :

x2 + 3x + 2 = 0

Factorising: (x + 1) (x + 2) = 0

Through factorising the quadratic equation,
you can equate (x + 1) = 0 or (x + 2) = 0.
Thus, x = -1 or x = -2.
This is made possible by factorising.

The demerit of this factorisation method, however, is that it takes time to figure out the numbers within the factors. Not all expressions can be easily changed to the factor form through simple "guessing".

NOTE: This post is talking about numbers and not matrices, which involve another concept of dealing with AB = 0.


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