Discussion

What is the remainder when \(x^2 - 7x + 15\) is divided by \(x-3\)?

Answer: A

By the Polynomial Remainder Theorem, the remainder when a polynomial P(x) is divided by \(x-a\) is P(a). Here, P(x) = \(x^2 - 7x + 15\) and a=3. We calculate P(3). \(P(3) = (3)^2 - 7(3) + 15 = 9 - 21 + 15 = 24 - 21 = 3\). The remainder is 3.