Consider the polynomial function g(x)=−x5−9x3−8x. Factor g(x) completely and determine all of its complex zeros. Which of the zeros of g are not x-intercepts of the graph of y=g(x)? Why do these zeros not correspond to a point on the x-axis? In general, what can be said about the similarities and differences between the zeros and the x-intercepts of the graphs of polynomial functions?
6.When a polynomial x4+x3−10x2−1 is divided by another polynomial, the quotient is x3−3x2+2x−8 and the remainder is 31. Find the other polynomial.
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