Home |
Polynomial ExpressionsA polynomial is an expression which involves various
powers of a variable. Some examples are: Here the coefficients (a's) can be any real number. The number n, which is an integer, is known as the degree of the polynomial. EX. is a polynomial of
degree 3, with leading coefficient 5, and constant term -2. Classifying PolynomialsPolynomials can be classified based on the degree (largest power), or based on the number of terms. 1 term = monomial EX. is a binomial of degree 5. _____________________________________________________________ Basic Operations on PolynomialsJust like with numbers, we often want to add, subtract, multiply and divide polynomials. Addition Adding polynomials is simply collecting like terms EX. Subtraction: To subtract two polynomials, you simply use the distributive law, then collect like terms. EX. Notice you distribute the minus sign. Multiplication: While adding and subtracting were fairly easy, multiply two polynomials can quickly become a headache. To multiply you must repeatedly apply the distributive law, then collect like terms. EX. Notice that the distributive law was applied four times to complete that single multiplication Division: FOILThere is a special case for multiplying polynomials, which occurs when you multiply a binomial times a binomial. In this case it is easier to use FOIL. EX. |