Answer:
The remainder is 25 ⇒ answer (C)
Explanation:
* The remainder will be the last number in the calculation
* From the picture the dividend is 3x³ + x² + 2x - 7 and x - 2 is the divisor
- In the synthetic calculation we use the coefficient of the dividend with the value of x when the divisor = 0
- From the picture the divisor is x - 2, when x - 2 = 0, then x = 2
∵ The coefficient of the dividend are 3 , 1 , 2 , -7
Step 1 : Write down the coefficients of the dividend , put x = 2 at the left
2 3 1 2 -7
_____________
Step 2 : Bring down the first coefficient to the bottom row.
2 3 1 2 -7
____________
3
Step 3 : Multiply it by 2, and carry the result into the next column.
2 3 1 2 -7
___6_________
3
Step 4 : Add down the column
2 3 1 2 -7
___6_________
3 7
Step 5 : Multiply it by 2, and carry the result into the next column
2 3 1 2 -7
___6_14_______
3 7
Step 6 : Add down the column
2 3 1 2 -7
___6_14_______
3 7 16
Step 7 : Multiply it by 2, and carry the result into the next column
2 3 1 2 -7
___6_14_32______
3 7 16
Step 8 : Add down the column
2 3 1 2 -7
___6_14_32______
3 7 16 25
∴ The quotient is (3x² + 7x + 16) and the remainder is 25