polynomial equation

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

2 practice marks

Original practice question

Find the solutions of $x^{3} - 3 x^{2} - 4 x + 12 = 0$.

Worked explanation

• Factor the polynomial

  \[x^{3} - 3 x^{2} - 4 x + 12 = \left(x - 3\right) \left(x - 2\right) \left(x + 2\right)\]

• Set each factor to zero

  \[x = -2, x = 2, x = 3\]

[-2, 2, 3]

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