Answer:

Sure, let's perform synthetic division step by step for the expression x^3 + 13x^2 + 32x + 20.

Step 1: Choose a root to divide by. Let's say we choose the root x = -1.

Step 2: Set up the synthetic division table:

-1 | 1 13 32 20

Step 3: Bring down the coefficient of the highest power term, which is 1, into the first row of the synthetic division table:

-1 | 1 13 32 20

|_________

1

Step 4: Multiply the root (-1) by the value in the first row, and write the result below the second row:

-1 | 1 13 32 20

|_________

1

-1

Step 5: Add the values in the second row:

-1 | 1 13 32 20

|_________

1

-1

________

0

Step 6: Multiply the root (-1) by the value in the third row, and write the result below the third row:

-1 | 1 13 32 20

|_________

1

-1

________

0 0

Step 7: Add the values in the third row:

-1 | 1 13 32 20

|_________

1

-1

________

0 0

________

0

Step 8: The result of the synthetic division is the last row of the table: 1x^2 - x + 0, which simplifies to x^2 - x.

Therefore, x^3 + 13x^2 + 32x + 20 divided by (x + 1) is equal to x^2 - x.

I hope this helps! Let me know if you have any further questions.

Step-by-step explanation:

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