When selling a certain commodity, the profit obtained depends on the advertising cost. The following equation shows how the profit y(in us dollars) varies with the advertising cost x (in tens of thousands of us dollars) when selling certain sports equipment

y=-141x³+5358x²-76560 0

When the advertising cost is $300,000 (x=30) the profit is?

Can we obtain the profit indicated in the answer above using a lower advertising budget?

ex: what is the polynomials whose zeroes can be an advertising budget lower than $300,000 if we want to obtain the same profit in Question1?

The quotient and remainder obtained when the polynomial in the above question is divided by the polynomial (x-30) is?

Setting the quotient obtained in the above question to zero and solving for x, we get the lower advertising budget that gives us the same profit as?

Hint: let y be the profit as a function of the advertising budget x. Suppose the advertising budget has x=k. Find the profit y(k)=L by plugging k into the profit function.

Reorganize the polynomial as a new polynomial y-L=0, and note that x=k is one of the zeroes of the polynomial. the other positive zero will give the cheaper advertising budget. Hint: in order to do that, first divide by x-k and get the quotient, then set the quotient to zero and solve. From here you can find a positive zero k, which is smaller than k. that zero will be the cheaper advertising budget.