Exercise 36 Page 178

Let's start by recalling the The Remainder Theorem.

The Remainder Theorem tells us that we can find the value of the polynomial function at x=k by dividing it by the binomial x-k. This allows us to evaluate the polynomial using synthetic division. Consider the given function. P(x) = - 6x^3+72x This function gives us the profit P in millions of dollars for a DVD manufacturer when x millions of DVDs are produced. According to the Remainder Theorem, we can find P(2) by dividing P(x) by x-2. Let's do this using synthetic division. Recall that we need to use a 0 for every missing x-term in the dividend polynomial.

Since the remainder is 96, we know that P(2)=96. This means that when 2 million DVDs are produced, the company earns $96 million. Recall that we can also find this value by evaluating the function.

As we can see, evaluating the function is easier for this case.