Answer:
See below.
Explanation:
I'll show you the process step-by-step.
The divisor is the root, so solve x - 1 = 0 for x.
x - 1 = 0
x = 1
Then use the coefficients of the polynomial in descending order as shown below.
1 | 6 11 -16 -11 10
|
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Copy the 6 vertically down to below the line.
1 | 6 11 -16 -11 10
|
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6
Now multiply the 1 at left by the first number on the bottom line, the 6, and write it above the line, one position up and to the right of where the 6 is.
1 | 6 11 -16 -11 10
| 6
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6
Add the 11 and the 6 and write the sum to the right of the 6 below the line.
1 | 6 11 -16 -11 10
| 6
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6 17
Repeat the process of multiplying the 1 by the rightmost number below the line and writing it diagonally above the line and adding.
1 × 17 = 17; -16 + 17 = 1
1 | 6 11 -16 -11 10
| 6 17
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6 17 1
Repeat the process of multiplying the 1 by the rightmost number below the line and writing it diagonally above the line and adding.
1 × 1 = 1; -11 + 1 = -10
1 | 6 11 -16 -11 10
| 6 17 1
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6 17 1 -10
Repeat the process of multiplying the 1 by the rightmost number below the line and writing it diagonally above the line and adding.
1 × -10 = -10; 10 + -10 = 0
1 | 6 11 -16 -11 10
| 6 17 1 -10
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6 17 1 -10 0
The zero below the line at the right means the remainder is 0.
The other numbers are the coefficients of the resulting polynomial quotient in descending order. The quotient is 1 degree less than the dividend.
The quotient is 6x³ + 17x² + x - 10
I hope the explanation is clear.
If you have questions, ask in the comments.