Answer
a. P(7) = 1
b. P(7) = 1
Work Step by Step
a. See attached picture below
The remainder is 1, so P(7) = 1
b. $P(x) = 6(7)^7 - 40(7)^6 + 16 (7)^5 - 200 (7)^4 - 60 (7)^3 - 69 (7)^2 + 13 (7) -139$
$P(x) = 4941258 - 4705960 + 268912 - 480200 - 20580 - 3381 + 91 - 139 = 1$