Adding and Subtracting Polynomials

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, $$2x^2 + 3x - 5$$ is a polynomial.

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

9x + 6

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, $$3x^2$$ and $$5x^2$$ are like terms.

The degree of a polynomial is the highest power of the variable in the expression. For example, in $$4x^3 + 2x^2 - x + 7$$ , the degree is 3.

Subtracting polynomials involves changing the signs of the terms in the polynomial being subtracted and then combining like terms.

4x^3 + 1x^2 - 3x + 1

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, $$3x$$ is a monomial, and $$2x^2 + 3x - 5$$ is a polynomial.

The sum of two polynomials $$P(x) + Q(x)$$ is obtained by adding their corresponding coefficients for like terms.

The horizontal asymptote of a polynomial function describes the behavior of the function as x approaches infinity. For example, for $$f(x) = 13(0.5)^x$$ , the horizontal asymptote is $$y = 0$$ .