Question

Use synthetic division to check that the number k is a lower bound for the real zeros of the function f.

k=-7; f(x)= 5x^3 - 8x^2 + x -5

Answer 1

see below

Explanation:

The signs on the bottom line alternate, so the value of k is, indeed, a lower bound.

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Comment on lower bound for this cubic

The signs of the coefficients alternate, so Descartes' rule of signs will tell you there are zero negative real roots. That is, 0 is a lower bound for real roots. No synthetic division is needed.