8-5 Dividing Polynomials The Division Algorithm states that Px) = D()Q%) + RX). Suppose that x-c is a factor of PX). Show that PC) = 0.
A. Because x - C is a factor of Px), RX) = 0. Substitute x-c for D\) to write Ply) = (x -c)QX). Then, we have P(c) = (c - COC) = 0.
B. Because x-c is a factor of Pl%), DX) = 0. Substitute x-c for Rx) to write Py) = (x - CQ(X). Then, we have P(c) = (c - QC) = 0.
C. Because DX) = x - , Q(x) = 0. Substitute x-c for R\) to write PW) = (-)RW). Then, we have PC) = (c- c)R(C) = 0.
D. Because D) = X-C, Q(C) = 0. Substitute x-c for Dx) to write Dx) = (x - CR%). Then, we have P(c) = (C - CA(C) = 0.