Section 14 Polynomials

1

• Section 1-4 Polynomials
• Polynomial an algebraic expression that involves
  only the operations of addition, subtraction, and
  multiplication by variables.
• Examples

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.
2

• Student Examples

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.
3

• 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.

This example has 3 terms 3x2,4x, and 2
4

• Degree maximum number of variables that appear
  as factors in any one term.
• Example

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
5

• Student Examples Name the polynomial and states
  its degree.

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
6

• 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.

7

• Homework
• Page 497
• Questions 1-20, 24-27, 31-38