Question

You use synthetic division to divide f(x) by (x−a) and find that the remainder equals 15. Your friend concludes that f(15)=a. Is your friend correct? Explain your reasoning.

a) Yes, my friend is correct.
b) No, my friend is not correct.

Answer 1

Your friend is not correct; synthetic division gives the remainder as the value of the function at x equals a. So if the remainder is 15 from synthetic division of f(x) by (x - a), it means that f(a) = 15, not f(15) = a.

Step-by-step explanation:

No, your friend is not correct. When you perform synthetic division of a polynomial f(x) by a binomial of the form (x - a), the remainder you obtain is the value of the polynomial evaluated at x = a, which is f(a). In this case, you found the remainder to be 15, which means that f(a) = 15, not f(15) = a. Therefore, if the remainder is 15, it tells us that the value of the polynomial f(x) when x equals a is 15, which is f(a) = 15, not the other way around as suggested by your friend.