Question

Precal, walkthrough please?
Find all the zeros of the function.
g(x)= x^4 +4x^3 -3x^2 +40x +208

Answer 1

Use synthetic division on the coefficients of each term of the polynomial (1, 4, -3, 40, 208), bearing in mind that the number of real zeroes in the solution will be equal to the number of sign changes or a number successively less than that by 2 at a time. For example, the first 2 coefficients are + and there is no sign change until the third coefficient (-3). So, so far, 1 sign change. The sign then changes back to + at the 4th term with +40, so there is the second and last sign change. So, there are either 2 or 0 real zeros to start with.