Factor theorem and polynomial roots

Practise factor theorem and polynomial roots with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $P(x)=x^3-2x^2-5x+6$. (a) Show that $x-1$ is a factor and factorise P completely. [2 marks] (b) Solve $P(x)=0$ and identify the y-intercept. [2 marks]

Worked explanation

• Part (a)

  $P(1)=1-2-5+6=0$. Division by $x-1$ gives $x^2-x-6=(x-3)(x+2)$.

• Part (b)

  Each factor is zero at one of $-2,1,3$. Substituting $x=0$ gives $P(0)=6$.

(a) $(x-1)(x-3)(x+2)$.; (b) $x=-2,1,3$; $(0,6)$.

Original VectorPaths practice; not an official VCAA question or marking rubric.