The profit earned by a company from selling its product is modeled (in thousand rupees) by the polynomial
P(x)=2(3x4−5x2+4x)−7,
where x represents the number of hundreds of units sold.
a. (i) Express P(x) in standard polynomial form.
b. (ii) Determine the degree and the leading coefficient of P(x).
c. (iii) Briefly comment on how the sign of the leading coefficient is expected to influence the behaviour of profit for very large positive values of x.