Polynomial operations include addition, subtraction, multiplication, and division. Factoring polynomials may be useful when solving polynomial equations. Theorems about polynomial functions are used to find information about a function that is helpful when sketching a graph of the function.
At A Glance
Polynomials can be added, subtracted, multiplied, factored, and divided.
- Polynomials are added or subtracted by combining like terms.
- Polynomials are multiplied by using the distributive property and properties of exponents.
- Polynomials are factored by using a variety of techniques, including grouping and formulas.
- Polynomials are divided by factoring or using algorithms for long division or synthetic division.
- The factored form of a polynomial expression can be used to solve the related equation.
- If the polynomial that defines a function is divided by , the remainder is .
- According to the factor theorem, for a polynomial that defines a function , is a factor if and only if .
- If is a rational zero of a polynomial function , then is a factor of the leading coefficient of the polynomial, and is a factor of the constant term of the polynomial.
- For a polynomial function , if and and have opposite signs, there is at least one real zero of between and .
- Every polynomial function of degree has at least one complex zero.