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Use synthetic division to determine the result given a root of x = 3 and (x³ - 2x² - 11x + 12).

Ox²-5x - 26
Ox²+x-8-12/(x-3)
Ox²-5x-26 + 90/(x-3)
Ox²+x-8

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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)

User Sanpas
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