In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (−6x^3+5x^2−8x+9)+(17x^3+2x^2−4x−13)

Key Concepts

Polynomial Addition

Polynomial addition involves combining like terms from two or more polynomials. Like terms are those that have the same variable raised to the same power. When adding polynomials, you simply add the coefficients of these like terms together while keeping the variable part unchanged.

Standard Form of a Polynomial

The standard form of a polynomial is a way of writing the polynomial such that the terms are arranged in descending order of their degrees. The degree of a term is determined by the exponent of the variable. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the standard form is already achieved as the terms are ordered from the highest degree (3) to the lowest (0).

Degree of a Polynomial

The degree of a polynomial is the highest exponent of the variable in the polynomial. It provides insight into the polynomial's behavior and the number of roots it may have. For instance, in the polynomial 3x^4 - 2x^2 + 7, the degree is 4, indicating that the polynomial can have up to four roots.