When you use synthetic division to divide x4+x3−2x2+2x−5 by 2x+1 , what is the value of the divisor? (1 point)

Question

Responses

2
2

12
1 half

−1
negative 1

−12

Answer 1

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 $-1/2$.