How do you divide #(x^2 + 7x – 6) / (x-6) # using polynomial long division?

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To divide (x^2 + 7x - 6) by (x - 6) using polynomial long division, follow these steps:

1. Write the dividend (x^2 + 7x - 6) and the divisor (x - 6) in long division format.
2. Divide the first term of the dividend (x^2) by the first term of the divisor (x). Write the result (x) above the line.
3. Multiply the divisor (x - 6) by the result (x) and write the product (x^2 - 6x) below the dividend.
4. Subtract the product (x^2 - 6x) from the dividend (x^2 + 7x - 6) and write the result (13x - 6) below the line.
5. Bring down the next term from the dividend (-6) and write it next to the result (13x - 6).
6. Divide the new dividend (13x - 6) by the first term of the divisor (x). Write the result (13) above the line.
7. Multiply the divisor (x - 6) by the result (13) and write the product (13x - 78) below the new dividend.
8. Subtract the product (13x - 78) from the new dividend (13x - 6) and write the result (72) below the line.
9. Since there are no more terms to bring down, the division is complete.
10. The quotient is the result written above the line, which is x + 13.
11. The remainder is the result written below the line, which is 72.

Therefore, (x^2 + 7x - 6) divided by (x - 6) using polynomial long division is equal to x + 13 with a remainder of 72.