Question 26
Giulio writes a polynomial $P_1(x)$ and another polynomial $P_2(x)$, a product of linear factors, whose degree is strictly greater. Dividing $P_2(x)$ by $P_1(x)$ gives remainder 0. Let $Q(x)$ be the quotient. Which statement is always true?
(A) $Q(x)$ can be constant.
(B) If $P_2(a)=0$, then $Q(a)=0$.
(C) There is a real number $a$ such that $P_2(a)=Q(a)=0$.
(D) $Q(x)$ certainly has degree less than $P_1(x)$.
(E) If $P_1(a)=0$, then $Q(a)=0$.
(A) $Q(x)$ can be constant.
(B) If $P_2(a)=0$, then $Q(a)=0$.
(C) There is a real number $a$ such that $P_2(a)=Q(a)=0$.
(D) $Q(x)$ certainly has degree less than $P_1(x)$.
(E) If $P_1(a)=0$, then $Q(a)=0$.