Precalculus upper and lower bounds

Question

X^3 -13x-12.

Need lowest upper bound and highest lower bound. Using synthetic division.

Lowest upper bound. -

Highest lower bound-

Answer 1

4l 1 0 -13 -12

_____4___16___12

1 4 3 0

Since there are no negative numbers in the bottom row, 4 is an upper bound for the real zeros.

-1l 1 0 -13 -12

_____1___-1___14

-1 1 -14 2

Since the signs alternate in the bottom row, -1 is a lower bound for the real zeros.

So, all real zeros of the given polynomial lie between -1 and 4.