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−1/2 1/2 -1 2
Answers
GPT-4o mini
To use synthetic division to divide the polynomial \(x^4 + x^3 - 2x^2 + 2x - 5\) by \(2x + 1\), you first need to express the divisor \(2x + 1\) in the form \(x - c\).
Starting from \(2x + 1 = 0\):
\[
2x = -1 \quad \Rightarrow \quad x = -\frac{1}{2}
\]
Since we are interested in the value of \(c\) such that we can perform synthetic division, we take \(c = -\frac{1}{2}\).
Thus, the value of the divisor is:
\(-\frac{1}{2}\)
Therefore, the correct response is:
\(-\frac{1}{2}\)
Starting from \(2x + 1 = 0\):
\[
2x = -1 \quad \Rightarrow \quad x = -\frac{1}{2}
\]
Since we are interested in the value of \(c\) such that we can perform synthetic division, we take \(c = -\frac{1}{2}\).
Thus, the value of the divisor is:
\(-\frac{1}{2}\)
Therefore, the correct response is:
\(-\frac{1}{2}\)