What is the simplified form of x^4 -81 /x+3

1 answer

To find the simplified form of the expression (x^4 -81)/(x+3), we can first factor the numerator using the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b). In this case, a = x^2 and b = 9.

Therefore, x^4 - 81 = (x^2 + 9)(x^2 - 9) = (x^2 + 9)(x + 3)(x - 3).

Now, substitute this factorization back into the original expression:

(x^4 - 81)/(x + 3) = [(x^2 + 9)(x + 3)(x - 3)]/(x + 3) = (x^2 + 9)(x - 3).

Therefore, the simplified form of the expression (x^4 - 81)/(x+3) is (x^2 + 9)(x - 3).