(a)

The polynomial function is and upper limit is x = 4.

The leading coefficient is 1 and the constant term is 1.

Possible rational zeros .

The original polynomial has two variations in signs.

The polynomial has one variations in sign.

From descartes rule of signs, the polynomial has either two or no positive real zeros, and it  has one negative or no negative real zeros.

By synthetic division, determine that is a rational zero or not.

The value of is not a zero because  the last row has either  positive or zero entries, we know that is an upper bound for the real zeros of f.

Thus, is an upper bound for the real zeros of f.

(b)

The polynomial function is and lower limit is .

From descartes rule of signs, the polynomial has either two or no positive real zeros, and it  has one negative or no negative real zeros.

\ \

By synthetic division, determine that is a rational zero or not.

The value of is not a zero because the last row has alternately positive and negative (zero entries count as positive or negative) entries, we know that is an lower bound for the real zeros of f.

Thus, is a lower bound for the real zeros of f.

(a) is an upper bound for the real zeros of f.

(b) is a lower bound for the real zeros of f.