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find a bound on the real zeros of the polynomial.

f(x)=x^4+2x^3-8x-7

every real zero of f lies between -? and ?

*pleasae show all work*

using synthetic division, dividing by x-a, take a look at the signs of the numbers in the quotient.

x-0: 1 2 0 -8 -7
x-1: 1 3 3 -5 -12
x-2: 1 4 8 8 9
all signs are positive, so all real roots are all less than 2.

Similarly, for negative values,
x+1: 1 1 -1 -7 0
x+2: 1 0 0 -8 9
x+3: 1 -1 3 -17 44
signs alternate, so all real roots are greater than -3

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