MathNet 2018-part-05 — 181 problems (EN–VI) Question 123

When the polynomial $p(x)$ is divided by the polynomial $x-18$, the remainder is 20. When the polynomial $p(x)$ is divided by the polynomial $x-20$, the remainder is 18. What is the remainder when the polynomial $p(x)$ is divided by the polynomial $(x-20)(x-18)$?

(A) 2018
(B) $-x-2$
(C) $x+2$
(D) $-x+38$
(E) $x+38$