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Need a bit of help on this

Need a bit of help on this-example-1
User Mbxtr
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7 votes

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

|

--------------------------------------

Copy the 6 vertically down to below the line.

1 | 6 11 -16 -11 10

|

--------------------------------------

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

--------------------------------------

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

--------------------------------------

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

--------------------------------------

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.

User Lhaferkamp
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