Question
When you use synthetic division to divide x^4+x^3−2x^2+2x−5 by 2x+1, what is the value of the divisor?
1/2
2
-1/2
-1
1/2
2
-1/2
-1
Answers
GPT-4o mini
To use synthetic division when dividing by a polynomial of the form \( ax + b \), we need to transform it to the form \( x - r \), where \( r \) is the root of the equation \( ax + b = 0 \).
Given the divisor \( 2x + 1 \), we can find its root:
1. Set \( 2x + 1 = 0 \).
2. Solve for \( x \):
\[
2x = -1 \implies x = -\frac{1}{2}.
\]
Thus, for synthetic division of \( x^4 + x^3 - 2x^2 + 2x - 5 \) by \( 2x + 1 \), we will use \( r = -\frac{1}{2} \).
The value of the root \( r \) is what you need to input for synthetic division, which corresponds to the option:
-1/2.
Given the divisor \( 2x + 1 \), we can find its root:
1. Set \( 2x + 1 = 0 \).
2. Solve for \( x \):
\[
2x = -1 \implies x = -\frac{1}{2}.
\]
Thus, for synthetic division of \( x^4 + x^3 - 2x^2 + 2x - 5 \) by \( 2x + 1 \), we will use \( r = -\frac{1}{2} \).
The value of the root \( r \) is what you need to input for synthetic division, which corresponds to the option:
-1/2.