Question

For each of these functions, find the least integer n such that f(x) is o(xn). If f(x)=(x⁴ + x² + 1)(x⁴ + 1), then the least integer n is

Answer 1

To find the least integer n such that f(x) is
`o(xn)` for the given function
`f(x) = (x^4 + x^2 + 1)(x^4 + 1)`, we calculate the highest degree term of the polynomial, which is x^8 after multiplying. The least integer n is 9.

Step-by-step explanation:

The task is to find the least integer n such that f(x) is o(xn).

The function given is
`f(x) = (x^4 + x^2 + 1)(x^4 + 1)`.

To solve this, we need to find the degree of the polynomial, which is the sum of the degrees of the two highest degree terms when they are multiplied.

By multiplying out f(x), we get
`x^8 + x^6 + x^4 + x^4 + x^2 + 1`.

Simplifying this, we see that the highest degree term is
`x^8`, which means the function is a polynomial of degree 8.

Therefore, the least integer n for which f(x) is o(xn) would be n = 9.