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−12negative 1 half121 half−1negative 12
Answers
GPT-4o mini
To find the value of the divisor in the context of synthetic division, we first need to convert the divisor \(2x + 1\) into a format suitable for synthetic division.
The divisor \(2x + 1\) can be rewritten in the form \(x - r\) by solving for \(r\):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
In synthetic division, we use the value of \(r = -\frac{1}{2}\) for \(2x + 1\).
Thus, the answer is:
\[
-\frac{1}{2}
\]
So, the correct response is \(-\frac{1}{2}\).
The divisor \(2x + 1\) can be rewritten in the form \(x - r\) by solving for \(r\):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
In synthetic division, we use the value of \(r = -\frac{1}{2}\) for \(2x + 1\).
Thus, the answer is:
\[
-\frac{1}{2}
\]
So, the correct response is \(-\frac{1}{2}\).