x^3+9x^2-2x+6/x-6- DIVIDE USING SYNTHETIC DIVISION
What is the quotient?
What is the remainder?
To divide using synthetic division, we first set up the problem like this:
6 | 1 9 -2 6
We take the coefficient of each term in the dividend (x^3 + 9x^2 - 2x + 6) and write them in order from highest to lowest degree, separating each coefficient with a space.
Then we place the divisor, x - 6, as the number outside the division symbol (in this case, 6).
Next, we bring down the first coefficient, which is 1:
6 | 1 9 -2 6
1
Next, we multiply the divisor (6) by the number we just brought down (1) and write the result under the next coefficient (9). We add these two numbers together:
6 | 1 9 -2 6
1 6
------
1
Next, we repeat the process by multiplying the divisor (6) by the sum we just obtained (6) and write the result under the next coefficient (-2). We add these two numbers together:
6 | 1 9 -2 6
1 6 24
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1 15
Finally, we repeat the process one more time by multiplying the divisor (6) by the sum we just obtained (15) and write the result under the last coefficient (6). We add these two numbers together:
6 | 1 9 -2 6
1 6 24 |
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1 15 22
Therefore, the quotient of the division is x^2 + 15x + 22, and the remainder is 22.