Answer:

The Long Division Method is used to divide one polynomial by another. The steps to perform the division are:

1. Write the dividend polynomial and the divisor polynomial, with the dividend polynomial being written above the divisor polynomial and a line drawn between them.

2. Divide the leading coefficient of the dividend polynomial by the leading coefficient of the divisor polynomial, and write this quotient as the first term of the quotient polynomial.

3. Multiply the divisor polynomial by the first term of the quotient polynomial, and write this product beneath the dividend polynomial.

4. Subtract the product from the dividend polynomial, and write the difference beneath the product.

5. Repeat steps 2-4, dividing the leading coefficient of the difference by the leading coefficient of the divisor polynomial, multiplying the divisor polynomial by the quotient, and subtracting the product from the difference, until the degree of the difference is less than the degree of the divisor polynomial.

6. The quotient polynomial and the final difference are the answer to the division problem.

Using this method, the division of (x² + 4x - 5) by (x-1) is as follows:

(x² + 4x - 5) ÷ (x-1) = x + 5 with a remainder of 0.

Therefore, the quotient of the given polynomials is x + 5, with a remainder of 0.