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 = -1; f(x) = 4x^3 - 2x^2 + 2x + 4; Lower bound?

Yes
No

Answer 1

Using synthetic division would require dividing f(x) by (x-k) or in this case, (x-(-1)).

Answer 2

so the answer is yes?

Answer 3

?

Answer 4

Graph the function to get

Answer 5

notice how the red line cuts through the x-axis between -1 and 0

Answer 6

so this visually shows us that x = -1 is a lower bound (it's the closest integer to the root and it is smaller than the root)

Answer 7

We can confirm it using synthetic division



The remainder is -4, so this proves that it's a lower bound