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Sign 3x5
do i half to factor this equation?

Using complete sentences, describe how you would analyze the zeros of the polynomial function f(x) = –3×5 – 8×4 +25×3 – 8×2 +x – 19 using Descartes’ Rule of Signs. (2 points)

No, you don’t.

By Descartes’ Rule of Signs, the number of sign changes in f(x) is the number of positive real zeroes or less than that by an even number. It also states that the number of sign changes in f(-x) is the number of negative real zeroes or less than that by an even number.

With f(x) = -3x^5 – 8x^4 + 25x^3 – 8x^2 + x – 19, we see that:
f(-x) = 3x^5 – 8x^4 – 25x^3 – 8x^2 – x – 19.

Then, f(x) has 4 sign changes and f(-x) has 1 sign change. Thus, f(x) has either 4, 2, or 0 positive real zeroes and f(x) has 1 negative real zero.

I hope this helps!