what is the remainder when x^3-2x^2-51x-108 is divided by x-2?
To find the remainder when a polynomial is divided by another polynomial, we can apply the Polynomial Remainder Theorem. According to this theorem, if we divide a polynomial f(x) by a binomial (x - a), the remainder can be found by substituting the value of a in the polynomial.
In this case, we need to find the remainder when f(x) = x^3 - 2x^2 - 51x - 108 is divided by x - 2. We can find the remainder by substituting x = 2 in the polynomial f(x).
Let's substitute x = 2 in f(x):
f(2) = (2)^3 - 2(2)^2 - 51(2) - 108
= 8 - 8 - 102 - 108
= -210
Therefore, the remainder when x^3 - 2x^2 - 51x - 108 is divided by x - 2 is -210.