Answer :
The correct representation in synthetic division form is option B -2 | 3 -4 9.
To perform synthetic division for the division problem (3x² - 4x + 9) / (x - 2), you should follow these steps:
Set up the synthetic division in the following form:
2 | 3 -4 9
Here, we take the divisor (x - 2) and set it equal to zero to find the value that goes outside the division symbol (2 in this case).
Write down the coefficients of the polynomial inside the division symbol (3, -4, 9) in descending order of their powers.
Perform synthetic division as follows:
Bring down the first coefficient (3).
Multiply the outside value (2) by the number you just brought down (3) and write the result below the next coefficient: 2 * 3 = 6.
Add the two numbers in the second column (-4 and 6) to get 2, then repeat the process: 2 * 2 = 4.
Add the two numbers in the third column (9 and 4) to get 13.
The result is shown in synthetic division form as:
2 | 3 -4 9
6 4
So, the correct representation in synthetic division form is option B:
-2 | 3 -4 9
To know more about division:
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