Chapter 5 Polynomials and Polynomial Functions - 5.5 Apply the Remainder and Factor Theorems - 5.5 Exercises - Skill Practice - Page 356: 35

Answer D

Given: $f(x)=4x^3+15x^2-63x-54$ We will plug in each value given and solve for $0$ $f(-9)\\=4(-9)^3+15(-9)^2-63(-9)-54\\=-2916+1215+567-54\\=-1188$ $f(-3)\\=4(-3)^3+15(-3)^2-63(-3)-54\\=-108+135+189-54\\=162$ $f(-1)\\=4(-1)^3+15(-1)^2-63(-1)-54\\=-4+15+63-54\\=20$ $f(3)\\=4(3)^3+15(3)^2-63(3)-54\\=108+135-189-54\\=0$ Hence, answer D is the correct answer.