In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (5x^2−7x−8)+(2x^2−3x+7)−(x^2−4x−3)

Key Concepts

Polynomial Addition and Subtraction

Polynomial addition and subtraction involve combining like terms from two or more polynomials. Like terms are those that have the same variable raised to the same power. When adding or subtracting, you simply add or subtract the coefficients of these like terms 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 5x^3 + 2x^2 - x + 4, the standard form is already achieved, with the highest degree term first.

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, a polynomial of degree 2 is quadratic and can have up to two real roots, while a degree 3 polynomial is cubic and can have up to three real roots.