Chapters found in Algebra 1

Algebra 1 is a second math course found in the high school and it can guide the person through many other expressions with the system of equations, real numbers, function, exponents, inequalities, rational and radical expression and polynomials.

The algebra math had been divided into 12 chapters and each one of these chapters had been divided into many lessons.    

This topic is the overview of the fundamental ideas with the tools available in the algebra

 It teaches

-         Solving the equation by learning solving the linear equation which has just one single variable

-         Solving of inequalities: learning about solving the inequalities using  just one single variable

-         Working with the units: this is a unit that teaches about the general concern  of modelling concern before diving in the modelling situation with many types of equation and function under algebra curriculum

-         Linear equation with graphs: you can learn about the linear equation which contains two different variables and how such can be represented in the graphical lines with value tables

-         Functions are the mathematical entities which assign the unique output in order to give the inputs. This is a topic meant to evaluate, to graph and to analyze while creating different functions types

-         Linear word problem: it is easy to solve such word problem which involves the real world which may be represented in the linear functions and equations

-         Sequences: you can learn different ways for which you may define the sequence by using or constructing the arithmetic with geometric sequences.

-         Equation system: learn the way of interpreting the solution system of the linear equations and to solve them.

-         Inequalities (graphs and system): within this system, the user will study the inequalities and then graph each one of them. This will help to get the solution and it helps to explore inequalities system with multiple inequalities at once and to use them in order to describe the situation in the real world.

-         Absolute value with piecewise function: in this chapter, the person will learn the way of graphing the absolute value function.

-         Rational exponents with the radical: in this chapter, you learn the expression of the rational exponent, the radical expression and the relationship which exist between the two forms of such representation

-         Exponential growth with decay:  you will learn the way that you may interpret basic exponential function and to construct, analyze or make up the graph.

-         Polynomials: you may learn how to subtract and to add polynomial  expression

-         Factorization: this helps to learn writing the polynomial expression with the product of the linear factors

-         Quadratics: this the system that teaches how  to analyze and to graph the quadratic functions

-         Irrational numbers: you can learn on the irrational numbers so that you can identify them easily.

All about Factorization

It is always better to start from scratch and know how the process in-built together and incorporated at places than to start working and return back to the basics.

What does the term Factorization mean?

It is the process of finding out factors of a polynomial or any equation. It is moreover like splitting of a complex term into two other numbers whose multiplication product if equal to the main term.

It can also be defined as the decomposition of a mathematical equation and is not necessarily applicable to polynomials, but also for Matrices and numbers

Why should one Factorize?

The main objective of factorizing is to reduce the complexity of the problem. The end results of Factorizing are something which cannot be further divided, thus breaking the equation to its simpler form.

The factorizing terms in their form can further be multiplied again to retain the original equations. This is also known as the expansion of polynomials. It is the best way to verify the solutions obtained after the factorizing process.

Equation

When should we Factorize?

Before moving on to factorization let us have a look at the factor theorem:

The factor theorem states that when a polynomial f(x) has a factor that is (x-k), it is only when f(x)=0

This means that the value of k that is obtained is a root of the polynomial.

Other uses of the Factor theorem are:

The factor theorem is used to remove known zeros from a polynomial while leaving all unknown zeros fixed, thus producing a lower degree polynomial whose zeros are easier to solve.

The method is:

1.    Use the factor theorem to conclude that the term (x-a) is a factor of f(x).

2.    Solve the polynomial g(x) =f(x)/f(x-a), for example using Long Division method of Polynomials or Synthetic Division method.

3.    Say that any root x is not equal to an of f(x) =0 is a root of g(x)=0.

4.    Since the polynomial degree of g is one less than that of the degree of f, it is "simpler" to find the remaining zeros.

Few Common Methods of Factorization

Listed below are the few commonly used methods for factorization:

Let us have a quick look at them

1. Highest Common Factor

The highest common factor of algebraic expressions is useful in factorization; and it is the product of the common prime factors, which includes both common numerical and algebraic factors.

2. Using the Common factor

ab+bc= b(a+c)

3. Using the Difference of the square formula

a^2-b^2= (a+b)(a-b)

By using the above method, you can easily find the factors of a number.

Real Life applications of Factorization

Finance

Commonly used in finance and accounting where the present value of the assets are determined and for stock evaluation. Its uses are also traced in bond trading and calculations.

Numerical Analysis

For complex and high ordered equations in derivations and formulae method of factorization is needed to reduce the complexity of the problem, thus getting a valid solution or a better and simpler form of the equation. Also, high tech algorithms use the basics of Factorizing.

Quadratic equations

Integration sums and wave equations always end up unexpectedly in a quadratic form and then the only factorization can reach for your help. It is also widely used for solving numerical and calculation unknown values when in higher than or equal to 2nd order format.