Chapter 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 406: 145

$ Remainder =134$

The Remainder Theorem states that if $f(x)$ is divided by $x-c$, the remainder is given by $f(c)$. Thus, if $P(x)=8 x^{4}-2 x^{3}+x-8$ is divided by $(x+2)$, the remainder will be equal to $P(-2)$. Hence, the remainder is $P(-2)=8(-2)^{4}-2(-2)^{3}+(-2)-8\\ P(-2)= 8(16)-2(-8)-10\\ P(-2)=134$ $\therefore Remainder =134$