Last updated on Sep 20, 2026

Solving Cubic Inequalities (VCE SSCE Mathematical Methods): Flashcards

📚Flashcards

Revision Notes Model Answers Quizzes Flashcards Exam Questions

Solving Cubic Inequalities

Practise the cards

10 cards from this deck

Show

Definition of cubic inequality

Degree 3 polynomial with inequality ( $\leq$ , $<$ , $\geq$ , $>$ )

Factor theorem: If $P(a) = 0$

$(x - a)$ is a factor

Purpose of polynomial division in cubics

Find remaining factors after factor theorem

Finding $x$ -axis intercepts

Set each factor to zero, solve for roots

Finding $y$ -axis intercept

Substitute $x = 0$ into function

Positive leading coefficient: cubic graph shape

Starts low (left), ends high (right)

Effect of repeated factors on graph

Turning points; touches but doesn't cross $x$ -axis

Where is graph for $P(x) \leq 0$ or $P(x) < 0$

On or below the $x$ -axis

Where is graph for $P(x) \geq 0$ or $P(x) > 0$

On or above the $x$ -axis

$(x-a)$ vs $(x-a)^2$ : graph behaviour at $x=a$

Crosses $x$ -axis vs touches (turning point)

Join 100,000+ SSCE students studying Flashcards with us.

Select your subjects, and get access to A+ resources today.

Solving Cubic Inequalities (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

Definition of cubic inequality

Factor theorem: If P(a)=0P(a) = 0P(a)=0

Purpose of polynomial division in cubics

Finding xxx-axis intercepts

Finding yyy-axis intercept

Positive leading coefficient: cubic graph shape

Effect of repeated factors on graph

Where is graph for P(x)≤0P(x) \leq 0P(x)≤0 or P(x)<0P(x) < 0P(x)<0

Where is graph for P(x)≥0P(x) \geq 0P(x)≥0 or P(x)>0P(x) > 0P(x)>0

(x−a)(x-a)(x−a) vs (x−a)2(x-a)^2(x−a)2: graph behaviour at x=ax=ax=a

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions