### 10.3 - Polynomial equations

Before reading this section you may want to review the following topics: To solve a polynomial equation, follow these steps:
• Ensure that the polynomial equation is in standard form, which is to have a polynomial on the left-hand-side of the equation and zero on the right-hand-side.

• Factor the polynomial on the left-hand-side completely using the methods of section 10.2.

• In section 4.1, we saw that if a · b = 0 then a = 0 or b = 0. Use this fact to set each factor equal to zero. This replaces a polynomial equation with a set of new equations that are either linear or quadratic.

• Solve each of the new equations. The solution set for the polynomial equation is the collection of all the solutions of the new equations.

Example: Solve the polynomial equation 16 x 3 − 13 x = 3.

Solution: First put the polynomial equation into standard form:
16 x 3 − 13 x − 3 = 0.
Factor the left-hand-side using the deflation method:
(x − 1) (4x + 1) (4 x + 3) = 0.
Set each factor equal to zero. This gives a set of equations:
x − 1 = 0
4x + 1 = 0
x + 3 = 0
Solve them. This gives a set of solutions:
x = 1
x = −¼
x = −¾
The solution set is x = {1,   −¼,   −¾}.

 Algebra Coach Exercises

If you found this page in a web search you won’t see the
Table of Contents in the frame on the left.
Click here to display it.