Cubic inequalities and endpoint inclusion · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Cubic sign charts — objective 1

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 22\right) \left(x - 17\right) \left(x - 16\right)\). Use a sign chart to analyse P.

Find the left endpoint of the bounded interval where \(\displaystyle P\ge 0\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Cubic sign charts — objective 1

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 21\right) \left(x - 19\right) \left(x - 17\right)\). Use a sign chart to analyse P.

Find the left endpoint of the bounded interval where \(\displaystyle P\ge 0\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Cubic sign charts — objective 2

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 21\right) \left(x - 19\right) \left(x - 17\right)\). Use a sign chart to analyse P.

Find the right endpoint of the bounded interval where \(\displaystyle P(x)\ge 0\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Cubic sign charts — objective 2

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 24\right) \left(x - 21\right) \left(x - 18\right)\). Use a sign chart to analyse P.

Find the right endpoint of the bounded interval where \(\displaystyle P(x)\ge 0\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Cubic sign charts — objective 3

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 24\right) \left(x - 21\right) \left(x - 18\right)\). Use a sign chart to analyse P.

Find the largest root.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Cubic sign charts — objective 3

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 27\right) \left(x - 22\right) \left(x - 20\right)\). Use a sign chart to analyse P.

Find the largest root.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Cubic sign charts — objective 4

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 24\right) \left(x - 20\right) \left(x - 19\right)\). Use a sign chart to analyse P.

Evaluate P at the midpoint of the last two roots.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Cubic sign charts — objective 4

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 27\right) \left(x - 22\right) \left(x - 20\right)\). Use a sign chart to analyse P.

Evaluate P at the midpoint of the last two roots.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →