Question

Which of the following correctly sets up the synthetic division for x³ − 4x² − 3 divided by x + 1?

A. -1|-1, -4, 0, -3.
B. -1|-1, -4, 1, -3.
C. 1|-1, -4, 0, -3.
D. 1|-1, -4, 1, -3.

Answer 1

The correct setup for the synthetic division of the polynomial x³ - 4x² - 3 by x + 1 is -1 | 1, -4, 0, -3, which corresponds with option A.

Step-by-step explanation:

The student asked which option correctly sets up the synthetic division for the polynomial x³ − 4x² − 3 divided by x + 1. To perform synthetic division, we first identify the zero of the divisor, in this case, -1 because x + 1 = 0 when x = -1. The coefficients of the dividend polynomial are then written next to this zero. If a term is missing in the polynomial, like the x-term in this case, a coefficient of 0 must be included for that term.

The correct setup for synthetic division in this context is therefore -1 | 1, -4, 0, -3, matching option A since the polynomial coefficients are positive 1 for x³, negative 4 for x², 0 for x (which is missing and thus has a coefficient of 0), and negative 3 for the constant term.