Question
Synthetic division is used to divide
−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)
Responses
The remainder is 1x−3.
The remainder is the fraction with numerator 1 and denominator x minus 3 .
There is no remainder.
There is no remainder.
The remainder is 1x+3.
The remainder is the fraction with numerator 1 and denominator x plus 3 .
The remainder is 1.
−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)
Responses
The remainder is 1x−3.
The remainder is the fraction with numerator 1 and denominator x minus 3 .
There is no remainder.
There is no remainder.
The remainder is 1x+3.
The remainder is the fraction with numerator 1 and denominator x plus 3 .
The remainder is 1.
Answers
GPT-4o mini
The “1” in the last row of the synthetic division represents the remainder of the division of the polynomial \(-x^3 + 3x^2 - 2x + 7\) by \(x - 3\).
In synthetic division, the last entry in the bottom row is the remainder when the polynomial is divided by the linear divisor.
So, the correct interpretation is:
**The remainder is 1.**
In synthetic division, the last entry in the bottom row is the remainder when the polynomial is divided by the linear divisor.
So, the correct interpretation is:
**The remainder is 1.**