Question

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.
k = 3; f(x) = 3x3 - 2x2 + 5x + 2; Upper bound?
yes or no?

Answer 1

I believe it is lower bound

Answer 2

Upper Bound
If synthetic division is performed by dividing by x-k, where k>0, and all the signs in the bottom row of the synthetic division are non-negative, then x=k is an upper bound (nothing is larger) for the zeros of the polynomial.
Lower Bound
If synthetic division is performed by dividing by x-k, where k<0, and the signs in the bottom row of the synthetic division alternate (between non-negative and non-positive), then x=k is a lower bound (nothing is smaller) for the zeros of the polynomial.
The zero in the bottom row may be considered positive or negative as needed.

Answer 3

Thank you so much!!

Answer 4

Np :)