MathDB
Some Synthetic Substitution

Source: 1976 AHSME Problem 19

May 18, 2014
algebrapolynomialalgorithmanalytic geometrygraphing linesslopemodular arithmetic

Problem Statement

A polynomial p(x)p(x) has remainder three when divided by x1x-1 and remainder five when divided by x3x-3. The remainder when p(x)p(x) is divided by (x1)(x3)(x-1)(x-3) is
<spanclass=latexbold>(A)</span>x2<spanclass=latexbold>(B)</span>x+2<spanclass=latexbold>(C)</span>2<spanclass=latexbold>(D)</span>8<spanclass=latexbold>(E)</span>15<span class='latex-bold'>(A) </span>x-2\qquad<span class='latex-bold'>(B) </span>x+2\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>8\qquad <span class='latex-bold'>(E) </span>15