The sign of a polynomial

Refere to khan academy: The sign of a polynomial

The sign of a polynomial between ANY two CONSECUTIVE roots is either always positive or always negative.

This is because polynomial functions are continuous functions (no breaks in the graph), which means that the only way to change signs is to cross the x-axis.

How to know the sign of a polynomial on each interval?

Just try a number in this interval and calculate the result, see its sign.

Example

Solve:

• Since the function value between two Zeros can be either Always negative or Always positive,
• So just simply try out any x-number between the two zeros: f(1)=-144 <0, so it’s negative.