The result of dividing (x³ - 2x² - 11x + 12) by x - 3 is: x² + x - 8 + 90/(x - 3)
Here's how to use synthetic division to determine the result given a root of x = 3 and (x³ - 2x² - 11x + 12):
1. Set up the division table:
x 1 -2 -11 12
3
2. Enter the root (3) outside the table:
x 1 -2 -11 12
3
3. Bring down the first coefficient (1):
x 1 -2 -11 12
3 1
4. Multiply the coefficient you brought down (1) by the root (3):
x 1 -2 -11 12
3 1 3
5. Add the product (3) to the next coefficient (-2):
x 1 -2 -11 12
3 1 1
6. Repeat steps 4 and 5 for subsequent coefficients:
x 1 -2 -11 12
3 1 1 -8
3 24
-11 40
90
7. The quotient is formed by the coefficients in the second row, ignoring the leading term (1):
Quotient: x² + x - 8
8. The remainder is the coefficient in the bottom right corner (90):
Remainder: 90
Therefore, the result of dividing (x³ - 2x² - 11x + 12) by x - 3 is: x² + x - 8 + 90/(x - 3)