The boundedness theorem shows how the bottom row of a synthetic division is used to place upper and lower bounds on possible real zeros of a polynomial function. Let P(x) define a polynomial function of degree n ≥ 1 with real coefficients and with a positive leading coefficient. If P(x) is divided synthetically by x - c and 

(a) if c > 0 and all numbers in the bottom row of the synthetic division are nonnegative, then P(x) has no zero greater than c; 

(b) if c

Use the boundedness theorem to show that the real zeros of each polynomial function satisfy the given conditions.

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P(x) = x² + x³ = x² + 3; no real zero less than -2