Question
When you use synthetic division to divide x4+x3−2x2+2x−5 by 2x+1 , what is the value of the divisor? (1 point)
Responses
−12
negative 1 half
2
2
−1
negative 1
12
Responses
−12
negative 1 half
2
2
−1
negative 1
12
Answers
GPT-4o mini
To use synthetic division for the polynomial \( x^4 + x^3 - 2x^2 + 2x - 5 \) divided by \( 2x + 1 \), we first need to find the zero of the divisor \( 2x + 1 \):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
In synthetic division, we use this value (\(-\frac{1}{2}\)) as the number we substitute into the synthetic division process.
Thus, the value we use when applying synthetic division is \( -\frac{1}{2} \).
The answer is therefore:
**negative 1 half**.
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
In synthetic division, we use this value (\(-\frac{1}{2}\)) as the number we substitute into the synthetic division process.
Thus, the value we use when applying synthetic division is \( -\frac{1}{2} \).
The answer is therefore:
**negative 1 half**.