Last updated on Sep 20, 2026

Solving Cubic Inequalities (VCE SSCE Mathematical Methods): Quizzes

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Solving Cubic Inequalities

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What degree polynomial is involved in a cubic inequality?

Degree three

If $P(a) = 0$ for a polynomial $P(x)$ , what can we conclude?

$(x - a)$ is a factor

How do you find the y-axis intercept of a cubic function?

Substitute $x = 0$

For a cubic with positive leading coefficient, how does the graph behave?

Starts low (left) & ends high (right)

What does a repeated factor like $(x - a)^2$ create on the graph?

Turning point at $x = a$

For $P(x) \leq 0$ , where should you look on the graph?

On or below the x-axis

For $P(x) \geq 0$ , where should you look on the graph?

On or above the x-axis

How should the final solution to a cubic inequality be expressed?

Set or interval notation

In the example $x^3 + x^2 - 5x + 3$ , what is the complete factorization?

$(x - 1)^2(x + 3)$

What is the solution to $x^3 + x^2 - 5x + 3 \leq 0$ from the worked example?

$(-\infty, -3] \cup \{1\}$

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