A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 4, 4, and 20. The bottom row has entries of 2, 2, 10, and 16.
Image with alt text: A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 4, 4, and 20. The bottom row has entries of 2, 2, 10, and 16.
A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 4, negative 4, and 4. The bottom row has entries of 2, negative 2, 2, and 0.
Image with alt text: A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 4, negative 4, and 4. The bottom row has entries of 2, negative 2, 2, and 0.
A synthetic division build with a divisor of 1. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 2, 4, and 10. The bottom row has entries of 2, 4, 10, and 6.
Image with alt text: A synthetic division build with a divisor of 1. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 2, 4, and 10. The bottom row has entries of 2, 4, 10, and 6.
A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 2, 0, and 10. The bottom row has entries of 1, 0, 6, and 8.
Image with alt text: A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 2, 0, and 10. The bottom row has entries of 1, 0, 6, and 8.
1 answer
To perform synthetic division for the expression \( 2x^3 - 2x^2 + 6x - 4 \) by the divisor \( x - 2 \), we need to use the value \( 2 \) as the divisor in synthetic division.
Let's carry out the synthetic division step-by-step:
Set up the synthetic division:
Write \( 2 \) on the left side for the divisor.
The coefficients of the polynomial \( 2x^3 - 2x^2 + 6x - 4 \) are \( [2, -2, 6, -4] \).
Perform synthetic division:
Bring down the leading coefficient \( 2 \).
Multiply \( 2 \) (the divisor) by \( 2 \) (the value just brought down) and write it under the next coefficient:
\[
2 \times 2 = 4
\]
Write \( 4 \) under \(-2\).
Add:
\[
-2 + 4 = 2
\]
Repeat the process:
Multiply \( 2 \) (the divisor) by \( 2 \) (the last result):
\[
2 \times 2 = 4
\]
Write \( 4 \) under \( 6 \).
Add:
\[
6 + 4 = 10
\]
Finally, multiply \( 2 \) (the divisor) by \( 10 \):
\[
2 \times 10 = 20
\]
Write \( 20 \) under \(-4\).
Add:
\[
-4 + 20 = 16
\]
The results show that the bottom row of synthetic division is \( [2, 2, 10, 16] \).
Therefore, the correct synthetic division option is:
A synthetic division display with a divisor of 2. The first row has entries of 2, negative 2, 6, and negative 4. The second row has entries of 4, 4, and 20. The bottom row has entries of 2, 2, 10, and 16.
1 answer