If F(x) = px² + qx + r and p + q + r = 0, which of the following is a factor of F(x)?

Correct answer: d x − 1

F(1) = p + q + r = 0, so x − 1 is a factor.

Why the other options are wrong

• a x − p: x − p would need F(p) = 0; p + q + r = 0 gives F(1) = 0.
• b x − q: x − q would need F(q) = 0; the condition does not give that.
• c x − 2: x − 2 would need F(2) = 0, that is 4p + 2q + r = 0; the given condition is different.