Section 1-4 Polynomials Polynomial: an algebraic expression that involves only the operations of addition, subtraction, and multiplication by variables. Examples: 1 This is a polynomial, subtraction and multiplication only. This is not a polynomial because of the division by the variable. This is not a polynomial because of the square-root of the variable.

Student Examples: 2 This is a polynomial, subtraction and multiplication only. This is not a polynomial because of the square-root of the variable. This is not a polynomial because of the absolute value of the variable. This is a polynomial, multiplication only. The square-root is only on the number. This is a polynomial, addition and multiplication only. This is not a polynomial because of the square-root of the variable.

Term: in an expression the parts that are separated by addition or subtraction are called terms. Example: When expressions have 1, 2, or 3 terms we give them special names: 1 term: monomial 2 terms: binomial 3 terms: trinomial When a polynomial has more than 4 terms we do not use a special name we just call it a polynomial. 3 This example has 3 terms: 3x^2,4x, and 2

Degree: maximum number of variables that appear as factors in any one term. Example: 4 This is a monomial that has a degree of 4 This is a monomial that has a degree of 3 This is a trinomial that has a degree of 10

Student Examples: Name the polynomial and states its degree. 5 This is a monomial that has a degree of 3 This is a monomial that has a degree of 9 This is a trinomial that has a degree of 3 This is a trinomial that has a degree of 7

When adding or subtracting polynomials we treat the problem as we are simplifying the expression by collecting like terms. The only difference is if we are subtracting we change the signs of the second polynomial. Examples: add or subtract. 6

Homework: Page 497 Questions 1-20, 24-27,