What Is Factorization?
Chapter Name : Factorization |
Sub Topic Code : 104_08_14_02_04 |
Topic Name : What Is Factorization? |
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Sub Topic Name : Factors Of The Form ( X+A) (X+B) |
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Introduction
If an algebraic expression is of the form ax2 + bx + c, then how can it be factorized if it is not in any of the identity forms?
Pre-Requisites:
Meaning of factors, how to factorize simple & direct algebraic expressions.
Activity:
Quadratic equations of single variable can generally be written in the form (x+a) (x+b). Try making a list of quadratic equations which cannot be written of that form
Real Life Question:
When there is an algebraic expression with single variable x, then is there a simpler way of factorizing it to get the solution? Like the path of a cricket ball.
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| (x + a) (x + b) | This is equal to : x2 + (a + b)x + ab |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Play car | You have those toy cars operated with remotes. The equation that governs their movement is quadratic with variable as time (t). To solve for it, this technique can be used |
Real life uses :
Many space related problems are quadratic equations. This technique may find its use after the complex equation is split into simple forms.
Places to visit :
Construction Site, Shopping Mall
Practical examples around us
| Examples | Explainations |
|---|---|
| Area of a plot | Many a times, the length of a plot may be given in terms of its breadth. In this case, the area will be expressed in the form of a quadratic equation with single variable. |
What you learn in Theory:
When there exists an equation of the form: x2 + px + q , there are two factors a & b of q (the constant term), such that, a + b = p ; ab = q, Then, the expression becomes : x2 + (a + b)x + ab
What you learn in Practice:
Quadratic expressions can be easily solved once the pattern is identified