Answer:
The other factor is a polynomial of degree 4 that contains the terms x^4, x^3y, x2y2, xy^3, and y^4. The coefficients of these terms are determined by the following formula1:
a_n = 1 a_k = a_(k+1) + (-1)^(n-k) for k = n-1, n-2, …, 1, 0
where n is the degree of the original expression (in this case, n = 5), and a_k is the coefficient of the term x(n-k)yk.
Using this formula, we can find the coefficients of the polynomial as follows:
a_4 = a_5 + (-1)^1 = 1 + (-1) = 0 a_3 = a_4 + (-1)^2 = 0 + 1 = 1 a_2 = a_3 + (-1)^3 = 1 + (-1) = 0 a_1 = a_2 + (-1)^4 = 0 + 1 = 1 a_0 = a_1 + (-1)^5 = 1 + (-1) = 0
Therefore, the polynomial is:
x^4 + x^3y + x2y2 + xy^3 + y^4
Hence, the expression x^5 - y^5 can be written as:
x^5 - y^5 = (x - y)(x^4 + x^3y + x2y2 + xy^3 + y^4)
You can also use the factoring calculator to check your answer.