Final answer:
The correct setup for the synthetic division of x³ – 4x² – 3 by x + 1 is -1, 1, -4, 0, -3, which corresponds to option b.
Step-by-step explanation:
To set up synthetic division for the polynomial x³ – 4x² – 3 divided by x + 1, we need to consider the coefficient of x in the divisor, which will be the first number in our synthetic division setup.
Since the divisor is x + 1, the number we use will be the opposite of the constant term in the divisor, which is -1.
Next, we list the coefficients of the polynomial we are dividing.
The polynomial x³ – 4x² – 3 has coefficients 1 (for x³), -4 (for x²), and for x, the coefficient is implicitly 0 because the x term is missing, followed by -3 (the constant term).
Therefore, the correct setup for synthetic division in this case is option b. -1, 1, -4, 0, -3.