A school is designing a triangular pennant whose area (in square centimetres) is modelled by the polynomial 5x3+10x2−40x.
a. (i) Factor out the greatest common factor from 5x3+10x2−40x.
b. (ii) Factor the resulting quadratic expression completely.
c. (iii) Using the factorised form, verify that x=2 and x=−4 make the polynomial equal to zero.
d. (iv) Solve 5x3+10x2−40x=0 for all real values of x.