Question
Which is the correct first line for dividing the function f left parenthesis x right parenthesis equals x cubed minus 12 x plus 16 by left parenthesis x minus 2 right parenthesis using synthetic division?
(1 point)
Responses
2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: 2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
negative 2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: negative 2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: 2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
negative 2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: negative 2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
(1 point)
Responses
2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: 2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
negative 2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: negative 2 Start Layout vertical line first Row 1 negative 12 16 modifying under second row empty with line End Layout
2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: 2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
negative 2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
Image with alt text: negative 2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout
Answers
GPT-4o mini
To perform synthetic division of the function \( f(x) = x^3 - 12x + 16 \) by \( x - 2 \), we identify the number to use in synthetic division, which is the root of the divisor \( x - 2 \). In this case, the root is \( 2 \).
The coefficients of the polynomial \( f(x) \) are:
- 1 (for \( x^3 \))
- 0 (for \( x^2 \))
- -12 (for \( x^1 \))
- 16 (constant term)
This means the correct setup for synthetic division will place \( 2 \) to the left of the vertical line, and the coefficients \( 1, 0, -12, 16 \) to the right.
Thus, the correct first line for the synthetic division is:
\[
2 \quad | \quad 1 \quad 0 \quad -12 \quad 16
\]
Therefore, the correct choice from the options given is:
**2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout**
The coefficients of the polynomial \( f(x) \) are:
- 1 (for \( x^3 \))
- 0 (for \( x^2 \))
- -12 (for \( x^1 \))
- 16 (constant term)
This means the correct setup for synthetic division will place \( 2 \) to the left of the vertical line, and the coefficients \( 1, 0, -12, 16 \) to the right.
Thus, the correct first line for the synthetic division is:
\[
2 \quad | \quad 1 \quad 0 \quad -12 \quad 16
\]
Therefore, the correct choice from the options given is:
**2 Start Layout vertical line first Row 1 0 negative 12 16 modifying under second row empty with line End Layout**