Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Defining, Translating, & Solving One-Step Equations

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:22 Linear
  • 1:28 Quadratic
  • 2:22 Cubic
  • 3:16 Polynomial
  • 4:28 Rational
  • 4:52 Radical
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to see the kinds of equations that you will come across most often in algebra. Learn to distinguish them by just looking for the identifying components of each equation.

Common Algebraic Equations

In algebra, there are some equation types that you will come across more often than others. You will find that if you can identify the type of equation that you are working with, then it becomes easier to work with the problem since you will know the properties of the equation. In this lesson we will cover six common algebraic equations.


The first one is called the linear equation. The general form of these equations is y = mx + b, where m and b are numbers and m cannot be zero. The way to identify these types of equations is to look for an x with no exponents. The x should be the only variable you see other than the y. You should not have any other exponents or square roots. The x is also always in the numerator, never in the denominator.

These equations are called 'linear' because when you graph them, you end up with a single line. So, to help you remember that you should only see one x, think of linear as having one line, and link the one line to the one x in your head. For example, y = 4x + 3 is a linear equation. Note that you see the x and no other x's. We can start building a table to keep all of these equations and their names organized.

Equations table

Quadratic Equation

The second common type of equation is the quadratic equation. This type of equation has a general form of ax^2 + bx + c = 0, where a, b and c are numbers and a is never zero. The other two letters, b and c, can be zero.

The key thing to look for here is the x^2. The exponent of 2 is the highest and you should not see any higher exponents in the equation. If the b is not a zero, then you will also see an x with no exponent. You should not see more x's than these two. An example of a quadratic equation is 4x^2 + 3x + 1 = 0. Do you see how the highest exponent is two? We can add this to our table.

equation table


The next type is the cubic equation, which has the general form of ax^3 + bx^2 + cx + d = 0, where a, b, c and d are numbers but a cannot be zero. The way to identify these types of equations is to look for the x^3. The 3 should be your highest exponent.

If b and c are not zero, then you will also have an x^2 and an x term, but your terms will never have an exponent higher than 3. For example, x^3 = 0 is an example of a cubic equation. Notice that 3 is the highest exponent here and our b, c and d are zero, but our a is a 1. Adding this information to our table, we get this.

equation table


While your linear, quadratic and cubic equations limited your highest exponent to 1, 2 and 3 respectively, the polynomial equation takes away that limit. A polynomial is of the form:


To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account