Synthetic division is used to divide

Question

−x3+3x2−2x+7 by x−3 .

The result is shown.

A synthetic division display with a divisor of 3. The first row has entries of negative 1, 3, negative 2, and 7. The second row has entries of negative 3, 0, and negative 6. The bottom row has entries of negative 1, 0, negative 2, and 1.

What does the “1“ in the last row mean?

(1 point)

Answer 1

In synthetic division, the last row represents the coefficients of the quotient polynomial and the remainder of the division.

In your case, the last row displays the coefficients of the result of the division, and the last entry, "1," is the remainder of the synthetic division when dividing \(-x^3 + 3x^2 - 2x + 7\) by \(x - 3\).

This means that after performing the division, there is a remainder of 1. Thus, we can express the result of the division as:

\[ -\frac{x^3 + 3x^2 - 2x + 7}{x - 3} = -x^2 + 0x - 2 + \frac{1}{x-3} \]

So, the "1" indicates that when you divide the polynomial \(-x^3 + 3x^2 - 2x + 7\) by \(x - 3\), you get a remainder of 1.