The volume (in cubic centimetres) of a rectangular box is given by V(x)=x^ 3 -9x^ 2…
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
The volume (in cubic centimetres) of a rectangular box is given by
V(x)=x3−9x2+26x−24,
where x centimetres represents one edge of the box.
(i) Show that x=2 makes the volume zero and state the corresponding linear factor of V(x).
(ii) Factorise V(x) completely.
(iii) Find all integral values of x for which the volume becomes zero.
(iv) Which of the values obtained in part (iii) can represent the actual edge length of the box? Give a reason for your answer.