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
2
2
12
1 half
−1
negative 1
−12
Responses
2
2
12
1 half
−1
negative 1
−12
Answers
GPT-4o mini
To use synthetic division with the divisor \(2x + 1\), we first need to set the divisor equal to zero to find the corresponding value to use in synthetic division.
\[
2x + 1 = 0
\]
Solving for \(x\):
\[
2x = -1
\]
\[
x = -\frac{1}{2}
\]
In synthetic division, we typically use the \(x\) value found from setting the divisor to zero. Therefore, for the divisor \(2x + 1\), the value we would use in synthetic division is \(-\frac{1}{2}\) (one-half but negative).
Thus, the answer to the question, which asks for the value of the divisor, is:
\(-\frac{1}{2}\) (1 half but negative), which corresponds to the response you provided as "1 half" indicating it is \(-1/2\).
\[
2x + 1 = 0
\]
Solving for \(x\):
\[
2x = -1
\]
\[
x = -\frac{1}{2}
\]
In synthetic division, we typically use the \(x\) value found from setting the divisor to zero. Therefore, for the divisor \(2x + 1\), the value we would use in synthetic division is \(-\frac{1}{2}\) (one-half but negative).
Thus, the answer to the question, which asks for the value of the divisor, is:
\(-\frac{1}{2}\) (1 half but negative), which corresponds to the response you provided as "1 half" indicating it is \(-1/2\).