In synthetic division, when you divide a polynomial by a linear factor of the form \( x - c \), the last number in the final row represents the remainder of the division.
In this case, you're dividing the polynomial \( -x^3 + 3x^2 - 2x + 7 \) by \( x - 3 \). If this is done correctly using synthetic division, the last number in the final row is the remainder of the division.
If the last row shows a "1," it means that the remainder of the polynomial division is 1. This implies that when you evaluate the polynomial \( -x^3 + 3x^2 - 2x + 7 \) at \( x = 3 \), the result is \( 1 \). In other words:
\[ (-3)^3 + 3(3^2) - 2(3) + 7 = 1. \]
So, to summarize, the "1" in the last row indicates that the remainder of the polynomial \( -x^3 + 3x^2 - 2x + 7 \) when divided by \( x - 3 \) is 1.
2 answers