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

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  • 0:22 Linear
  • 1:28 Quadratic
  • 2:22 Cubic
  • 3:16 Polynomial
  • 4:28 Rational
  • 4:52 Radical
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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.

Linear

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

Cubic

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

Polynomial

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:

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