All zeros of the polynomial function or solve the given polynomial function. Use the Rational Zero Theorem, Descarte's Rule of Signs 3x^3-8x^2-8x+8=0?

polynomial-function
rational-zeros
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#1

all zeros of the polynomial function or solve the given polynomial function. Use the Rational Zero Theorem, Descarte’s Rule of Signs 3x^3-8x^2-8x+8=0 ?

Answer:

Look at the sign changes first to find # of positive zeros, it goes from + to - to - to +, so how many variations of signs are there? 2, so by Descartes Rule of Signs, there are ether 2 positive real zeros or 0 real zeros (you subtract the number by an even integer).
To find # of negative real zeros, stick (-1) in for x and find number of sign variations, it goes from - to - to - to +, so there is 1 neg. real zero (if the number was 2, there would be either 2 or 0 possible negative zeros, but since 1-2= -1, there can’t be -1 real negative zeros)