Compute the income tax due on taxable income entered by the user, given the data as shown in the following table. Be sure to include error checking to make sure the user does not enter a negative number. Assume all entries are integer values.

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To compute the income tax due on taxable income entered by the user, we first need to determine the tax bracket that the user's income falls into. Once we know the tax bracket, we can use the corresponding tax rate to calculate the income tax amount.

Here's an example table to illustrate the tax brackets and rates:

Taxable Income Tax Rate
-------------------------------
Up to $10,000 10%
$10,001 - $40,000 15%
$40,001 - $80,000 20%
Above $80,000 25%

To solve this problem, we can break it down into the following steps:
1. Prompt the user to enter their taxable income.
2. Check if the input is a positive integer. If not, display an error message and prompt the user to enter a valid taxable income.
3. Compare the user's taxable income to the income thresholds of the tax brackets to determine the tax bracket.
4. Once the tax bracket is determined, use the corresponding tax rate to calculate the income tax amount.
5. Display the income tax due to the user.

Here's a Python code snippet that implements the above steps:

```python
def compute_income_tax():
while True:
try:
taxable_income = int(input("Enter your taxable income: "))
if taxable_income < 0:
print("Error: Taxable income cannot be negative.")
else:
break
except ValueError:
print("Error: Invalid input. Please enter a valid positive integer.")

if taxable_income <= 10000:
tax_rate = 0.1
elif taxable_income <= 40000:
tax_rate = 0.15
elif taxable_income <= 80000:
tax_rate = 0.20
else:
tax_rate = 0.25

income_tax = taxable_income * tax_rate

print("Income tax due: $", income_tax)

compute_income_tax()
```

This code validates the user input, determines the tax bracket, calculates the income tax, and displays the result. It also includes error checking to ensure the user enters a positive integer as taxable income.