Answer
$P(4) = 16$
Work Step by Step
RECALL:
The remainder when $P(x)$ is divided by $(x-c)$ is $P(c)$.
Thus, when $P(x)=4x^6-25x^5+35x^4+17x^2$ is divided by $x-4$, the remainder is given by $P(4)$.
Evaluate $P(4)$ to obtain:
$P(4) = 4(4^6) - 25(4^5)+35(4^4)+17(4^2)
\\P(4) = 16,384-25,600+8,960+272
\\P(4)=16$
Perform synthetic division to check if the remainder is really 16:
