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 −1 negative 1 −12 negative 1 half 12
Answers
GPT-4o mini
In synthetic division, the divisor is typically expressed in the form \(x - c\). However, in this case, your divisor is \(2x + 1\).
To apply synthetic division to this expression, we first need to rewrite the divisor. We set \(2x + 1 = 0\) to find \(c\):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
So, for synthetic division with respect to the divisor \(2x + 1\), we will use \(c = -\frac{1}{2}\).
Now, since the question asks for the value of the divisor itself, and given the choices provided, none of them directly correspond to the original form of the divisor. However, if we follow what we've found and use the divisor \(2x + 1\) evaluated at the point \(x = -\frac{1}{2}\):
\[
2\left(-\frac{1}{2}\right) + 1 = -1 + 1 = 0
\]
This is the point where the synthetic division applies.
If we look instead just at the structure of the divisor \(2x + 1\), the relevant coefficient of 2 in front of \(x\), it appears your options are somewhat misleading as they mostly deal with numerical values unrelated directly to synthetic division.
Thus, the relevant answer is based on the constant associated with the divisor itself, which corresponds to the coefficient before \(x\):
**The divisor's coefficient is 2, according to the standard interpretation.**
To apply synthetic division to this expression, we first need to rewrite the divisor. We set \(2x + 1 = 0\) to find \(c\):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
So, for synthetic division with respect to the divisor \(2x + 1\), we will use \(c = -\frac{1}{2}\).
Now, since the question asks for the value of the divisor itself, and given the choices provided, none of them directly correspond to the original form of the divisor. However, if we follow what we've found and use the divisor \(2x + 1\) evaluated at the point \(x = -\frac{1}{2}\):
\[
2\left(-\frac{1}{2}\right) + 1 = -1 + 1 = 0
\]
This is the point where the synthetic division applies.
If we look instead just at the structure of the divisor \(2x + 1\), the relevant coefficient of 2 in front of \(x\), it appears your options are somewhat misleading as they mostly deal with numerical values unrelated directly to synthetic division.
Thus, the relevant answer is based on the constant associated with the divisor itself, which corresponds to the coefficient before \(x\):
**The divisor's coefficient is 2, according to the standard interpretation.**