Determine whether x = 1 and x = -6 are zeros for the function using the specified method.

Question

f(x) = x³ - 52x - 96

(A) Using synthetic division

(B) Plug into f(x) directly.

Answer 1

x = 1

Synthetic Division:

The remainder is -147 so it is not a zero

Plug into f(x) directly:

(1)³ - 52(1) - 96 = -147 not a zero because the result is not 0

x = -6

Synthetic Division:

It is a zero because the remainder is 0.

Plug into f(x) directly:

(-6)³ - 52(-6) - 96 = 0 so it is a zero because the result is 0