Answer: C) 77
Remainder theorem: If p(x) is divided by (x-k), then the remainder is p(k)
In our case, p(x) = x^3-5x^2-4x+7 and k = 7
p(x) = x^3-5x^2-4x+7
p(7) = (7)^3-5(7)^2-4(7)+7
p(7) = 77
The remainder is 77
Side note: The nonzero remainder means x-7 is not a factor of x^3-5x^2-4x+7.
You can also use polynomial long division (see figure 1) or synthetic division (see figure 2). The figures are attached in the image below.
