Last updated on Sep 20, 2026

Solving Cubic Equations (VCE SSCE Mathematical Methods): Quizzes

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Solving cubic equations

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What does the null factor theorem state?

If a product equals zero, a factor is zero

What is the maximum number of real solutions a cubic equation can have?

Three solutions

Solve $(x - 5)(x + 2)(x + 4) = 0$

$x = 5, -2, -4$

What should you check for first when solving cubic equations?

Common factors

The grouping method works by arranging terms into what?

Pairs that share factors

What does the factor theorem tell us about $P(x)$ if $P(a) = 0$ ?

$(x - a)$ is a factor of $P(x)$

In what order should you test values when using the factor theorem?

$\pm 1, \pm 2, \pm 3$

If the remaining quadratic has a negative discriminant, how many real solutions does the cubic have?

One real solution

What is the first step in solving cubic equations?

Factorise the expression

For $2x^3 - x^2 - x = 0$ , what should be factored out first?

$x$

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