Last updated on Sep 20, 2026

Division and Factorisation of Polynomials (VCE SSCE Mathematical Methods): Quizzes

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Division and Factorisation of Polynomials

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In $P(x) = D(x)Q(x) + R(x)$ , what is $Q(x)$ called?

The quotient

What constraint applies to remainder $R(x)$ in polynomial division?

Degree less than divisor or zero

What is the remainder when $P(x)$ is divided by $x - 5$ ?

$P(5)$

If $P(3) = 0$ , what can we conclude?

$x - 3$ is a factor of $P(x)$

What is the factorisation of $x^3 + a^3$ ?

$(x + a)(x^2 - ax + a^2)$

What is the factorisation of $x^3 - a^3$ ?

$(x - a)(x^2 + ax + a^2)$

Find remainder when $P(x)$ is divided by $2x + 1$ .

$P(-\frac{1}{2})$

If $-\frac{\alpha}{\beta}$ is a rational root of $P(x)$ , what divides the leading coefficient?

$\beta$

How should $2x^3 - 5x + 1$ be written for long division?

$2x^3 + 0x^2 - 5x + 1$

What is the quotient when $x^3 + x^2 - 14x - 24$ is divided by $x + 2$ ?

$x^2 - x - 12$

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