Consider an example 2x²+6x,

We know that 2x² and 6x our connected by addition so, in this equation 2x² and 6x are terms of algebraic expression 2x²+6x

2x² + 6x ← Mathematical expression

Until now we have studied the expression and terms now there is another mathematical term factor. So what does the word factor mean in algebra or in a mathematical expression?

Factors are part of the expression, connected with multiplication. For example 7xy here, 7 is multiplied by x and Y.

There is one more part to a mathematical expression that is coefficient, so what is a coefficient in math?

A coefficient is considered to be a number that is multiplied by a variable in a mathematical expression.

Let’s take 3x,

Here the number is 3 and the variable is x, so the coefficient of our variable x will be 3.

Coefficient of a Term

Similarly, if we see 3x as a term then the coefficient of a term 3x will also be 3.

Coefficient → 3 x

This is the last one to a mathematical expression, Constant is the single number in an expression without having any variable.

So from the above facts, we see that terms, factors, constant and coefficient makes a mathematical expression, each part of the expression has their own function and labels.

By now we know about the parts of a mathematical expression but there is more to it.

An algebraic expression can be classified mainly into three types:

Monomial Expression

An expression with only one term is known as a monomial expression.

For example: 3x, 7y, 4xy.

Binomial Expression

If an expression that has two unlikely terms is a binomial expression.

For example 3x + 8, 7yx + 65.

Polynomial Expression

A polynomial in algebra are expression with more than one term but that term should not negative exponent and

All exponents in a polynomial must be positive.

There should not be a radical on a variable in it.

The denominator should not be a variable.

For examples: 50x + 2xy + 30x + 45y + 1.

Ever wondered what is the difference between an algebraic expression and algebraic equation?

The algebraic expression has no right and left sides or equal to sign but an equation has equal to sign to prove that that particular equation is equal to the other side of the equation.

Earlier we have studied the expression, so if we put two expressions one on the right side and the other on the left with the equal to sign in between then we get the equation.

The word equation originated from a Latin word æquare which means “to make equal”, so equations are based on a mathematical concept of making both one part of the expression equal to other parts.

Let’s take a + b = c.

So both the sides should be equal to one another

Polynomial Equations

All algebraic equations consist of the polynomial equation which has a variable coefficient and exponents.

For example 2x+3y+1

Factorization of Polynomial

Factorization is the most important and common methods in mathematics. The process of finding factors to a value is called factorization. Different methods to factorize the polynomials are the Greatest Common Factor (GCF), Grouping Method, Sum or difference in two cubes, Difference in two squares method, General trinomials, and trinomial method.

Let’s take an example to

Factorize x² + 5x + 6 by splitting the middle term

From the name of the method only we realize that we have to split the middle term in the equation so, here the equation consists of three terms.

We need to find two numbers such that (let’s take a,b)

(a + b =5) Splitting the 5 into two numbers

and (ab = 6)

So that we can write x² + 5x + 6 as x² + 3x + 2x + 6

Which then be written as

x²+ 3x + 2x + 6

= x(x + 3) + 2(x + 3)

= (x + 3)(x + 2)

So, x+3 and x+2 are the factors of the polynomial x² + 5x + 6.

Quadratic Equations

A polynomial equation with a degree 2 in one of the variable is a quadratic equation. A standard form of a quadratic equation is ax²+bx+c=0 where a is not equal to 0.

Cubic Equation

Cubic equations are also polynomial with degree 3 on a variable it can be written as

ax³+bx²+cx+d=0

And there is another one known as trigonometric equations which are also as an

algebraic equation.

There is a name for people who specialize in algebra, they are known as an algebraist and that’s not the only fun thing about algebra. Basketball is also associated with algebra. The best example of it is when an actor of a Hollywood movie big uses a basketball analogy to help a kid in a movie solving homework about algebra isn’t that funny?

FAQ (Frequently Asked Questions)

1. Can a Number be an Algebraic Expression?

No, a number alone cannot be an algebraic expression because to be an expression there should be two terms with a mathematical operation.

For example, 3x+7y which has an operation addition between both the term and variable x and y.

So an expression needs to have a variable with an operation to be an expression and a number alone cannot become an expression.

2. How is Algebra Invented?

We know that algebra includes letters and numbers when combining these two we reach an equation which helps us in finding the answer to many things. It all started when the Greeks founded the geometric algebra in which they used sides of geometric objects, which mainly consisted of lines of associated letters in order to represent and form the terms. Thus, through this new kind of process and forms, they found algebra and made it possible to find out solutions to equations by making use of this same process and they called it ‘the application of area's.