Question

Identify the leading coefficient, and classify the polynomial by degree and by number of terms. $$x-x^{3}$$

Short answer

The leading coefficient is -1, the degree of the polynomial is 3, and the number of terms is 2.

Step-by-step solution

Reordering Polynomials

Reorder the given polynomial in standard form: The polynomial should be written with descending powers of the variable, therefore, it becomes \( -x^{3} + x \)

Identifying and Classifying

Identify the leading coefficient, degree, and number of terms. The leading coefficient is the coefficient of the highest degree term, which is -1 in this case. The degree of the polynomial is 3, as it is the highest exponent. The number of terms is 2, as the polynomial can be broken down into two distinct parts, separated by the symbol +.