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

$P(x) = D(x)Q(x) + R(x)$

Degree less than divisor or zero

Divide, multiply, subtract, repeat

Pleft(-rac{alpha}{eta} ight)

$P(alpha)$

If $P(alpha) = 0$, then $x - alpha$ is a factor

$x^3 - a^3 = (x - a)(x^2 + ax + a^2)$

$x^3 + a^3 = (x + a)(x^2 - ax + a^2)$

eta|leading coeff., $alpha$|constant term

Include with coefficient zero