IXL - Graph solutions to higher-degree inequalities (Precalculus practice)

Solve for

and graph the solution.

(

–

)

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

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Learn with an example

question

Solve for

and graph the solution.

(

)

Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of a segment, ray, or line to delete it.

key idea

A polynomial inequality can be written as

(

)

(

)

≥

(

)

(

)

≤

where

(

)

is a polynomial.

The roots of

(

)

separate the

-axis

into intervals. On each interval,

(

)

is either entirely positive or entirely negative.

This diagram is called a sign chart. It shows whether

(

)

is positive or negative on each interval between its roots. (In this example,

(

)

(

)

(

–

)

(

–

)

solution

Look at the polynomial inequality:

(

)

Since the inequality is strict (>), the solution to the inequality is the set of values where the polynomial

(

)

is positive.

Create a sign chart.

Start by marking the roots of the polynomial on a number line. You can find the roots by solving

(

)

The only root is

–

The root separates the number line into two intervals. Find the sign of the polynomial on each of the two intervals.

Since the exponent 3 is odd,
(
x
+
6
)
3
is negative if
x
<
–
6
and positive if
x
>
–
6
.

Graph the solution.

Graph the interval where the polynomial is positive. Be sure to exclude the endpoint of the interval since the polynomial is zero there.

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

P.1Graph solutions to quadratic inequalities

F.1Find the roots of factored polynomials

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