According to the Remainder Theorem, the value of the polynomial f(x) at x = a is the remainder when this polynomial is divided by x- a. Synthetic division can be used to obtain the remainder.
See the attached file for the synthetic division of the given polynomial by x - 5 and x + 4. The first row is the coefficients of the polynomial and the last row is the coefficients of the quotient, except for the last number, which is the remainder.
f(5) = 37 and f(-4) = -124