Question

what is the degree of the polynomial ? what is the leading coefficient ? describe the end behavior of each function. f(x)=x^4-2x^2+2

Answer 1

4th degree polynomial with leading coefficient of 1.

As x goes to negative or positive infinity, y goes to positive infinity in both cases.

Explanation:

The degree of a polynomial is the highest exponent on the variable. Here it is 4.

The leading coefficient is the coefficient on the the term with the highest degree, Here there is none so it is 1.

The end behavior is how x and y behave at negative and positive infinity. When graphed, this equation has a W shape. This means at each end y goes to positive infinity.