This document introduces algebraic expressions and polynomials. It defines algebraic expressions as involving variables, constants, or both. Polynomials are defined as the sum of polynomial terms, where a term is a constant or the product of a constant and variables raised to positive integer powers. The document provides examples of evaluating algebraic expressions and describes relationship machines to represent expressions visually. Key polynomial terminology is introduced, such as monomial, binomial, trinomial, coefficients, constant terms, and degree. Examples are given to classify expressions and polynomials.

2. Purpose:
1.) Introduce algebraic expressions and their
meaning.
2.) Evaluate algebraic expressions.
3.) Introduce polynomials.
4.) Learn the vocabulary of polynomials.

3. Algebraic expressions – are
expressions involving variable,
constant or a combination of
variable and constant.

4. TABLE 1 (Values of Expressions)
Expression/x 1 2 3 4 5
x + 5 8
7x 14
7x + 5
x2+ 7x + 5

5. TABLE 1 (Values of Expressions) - Answers
Expression/x 1 2 3 4 5
x + 5 6 7 8 9 10
7x 7 14 21 28 35
7x + 5 12 19 26 33 40
x2+ 7x + 5 13 23 35 49 65

6. TABLE 2 (Operations on x in Expressions)
Expression Operations in x
x + 5 Add 5
7x
7x + 5
x2 + 7x + 5
4x - 3
4x3
3x2 + 4

7. TABLE 2 (Operations on x in Expressions)- Answers
Expression Operations in x
x + 5 Add 5
7x Multiply by 7
7x + 5 Multiply by 7, add 5 to the product
x2 + 7x + 5
Square input, multiply input by 7, add
the square and the product, add 5 to
the sum
4x - 3
Multiply by 4, subtract 3 from the
product
4x3 Cube input, multiply the cube by 4
3x2 + 4
Square input, multiply the square by 3,
add 4 to the product.

8. Draw a relationship machine for each
of the following expressions:
a. 7x + 5

9. Draw a relationship machine for each
of the following expressions:
a. 7x + 5
x
Multiply by 7
Add 5 to the product
7x + 5

10. Draw a relationship machine for each
of the following expressions:
b. 3x2 + 4

11. Draw a relationship machine for each
of the following expressions:
b. 3x2 + 4
x
Square input
Multiply square by 3
Add 4 to the product
3x2 + 4

12. Draw a relationship machine for each
of the following expressions:
c. 4x – 3

13. Draw a relationship machine for each
of the following expressions:
c. 4x – 3
x
Multiply by 4
Subtract 3 from the product
4x – 3

14. Draw a relationship machine for each
of the following expressions:
d. 5x2 + 8

15. Draw a relationship machine for each
of the following expressions:
d. 5x2 + 8
x
Square input
Multiply square by 5
Add 8 to the product
5x2 + 8

16. Vocabulary of Polynomials
A polynomial is a mathematical expression
consisting of a sum of polynomial terms.
A polynomial term is a constant or a product
of a constant and one or more variables
raised to positive integral power.
A constant is a number. For example 5 is a
constant, but x and 5x are not constants.

17. Vocabulary of Polynomials
A monomial is a polynomial with exactly one
term.
A binomial is a polynomial with exactly two
terms.
A trinomial is a polynomial with exactly
three terms.

18. Vocabulary of Polynomials
A numerical coefficient of a term is the
constant factor of the term.
A constant term in a polynomial is the term
that contains no variables. If there is no such
term, then the constant term is 0.

19. Vocabulary of Polynomials
A linear polynomial with only one variable
is a polynomial in which the highest power
on the variable is one. The one is often
implied than written.
A quadratic polynomial with only one
variable is a polynomial in which the highest
power on the variable is two.

20. Vocabulary of Polynomials
The degree of the polynomial with only one
variable is the highest power on the variable.
Linear polynomials have a degree of 1.
Quadratic polynomials have a degree of 2.

21. Direction: Write YES if it is an algebraic
expression or a polynomial and NO if it is not.
Given
Algebraic
Expression
Polynomial
1.) 4𝜋
2.)
1
3𝑥
3.) 4x + 3
4.) twice x
5.) 10

22. Direction: Write YES if it is an algebraic expression or a
polynomial and NO if it is not. - Answers
Given
Algebraic
Expression
Polynomial
1.) 4𝜋 YES NO
2.)
1
3𝑥
YES NO
3.) 4x + 3 YES YES
4.) twice x NO NO
5.) 10 YES NO