Higher degree equations

A higher degree equation is an equation with terms greater than a degree of 2.

3rd degree equations

Example 1

Solve the third degree equation

Let us take a common factor, in which case we get one zero point x = 0 with zero-product property and a quadratic equation, from which the remaining solutions x = -1 and x = 2 are obtained.

Example 2

Solve the third degree equation

Now it is not possible to take a common factor from all the terms. So we use grouping.

The equation has only one solution x = 2, since the quadratic factor has no zeros.

If the equation cannot be modified into a factor form and it is not a power equation, we do not have the tools to solve the equation. Of course, calculators and calculator software can solve all of these equations.

Fourth degree equation

Example 3

Solve the fourth degree equation

We substitute

into equation

Now we substitute back

There are four solutions to the equation. x = -2, x = -1, x = 1 and x = 2

Turn on the subtitles if needed