Algebraic Extensions of Order of

Operations

to Polynomials

Purpose:

1.) Introduce algebraic expressions and their meaning.

2.) Evaluate algebraic expressions.

3.) Introduce polynomials.

4.) Learn the vocabulary of polynomials.

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

TABLE 1 (Values of Expressions)

Expression/x 1 2 3 4 5

x + 5 8

7x 14

7x + 5

x2+ 7x + 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

TABLE 2 (Operations on x in Expressions)

Expression Operations in xx + 5 Add 5

7x7x + 5

x2 + 7x + 54x - 34x3

3x2 + 4

TABLE 2 (Operations on x in Expressions)- Answers

Expression Operations in xx + 5 Add 5

7x Multiply by 7

7x + 5 Multiply by 7, add 5 to the product

x2 + 7x + 5Square 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.

Draw a relationship machine for each of the following expressions:

a. 7x + 5

Draw a relationship machine for each of the following expressions:

a. 7x + 5x

Multiply by 7Add 5 to the product

7x + 5

Draw a relationship machine for each of the following expressions:

b. 3x2 + 4

Draw a relationship machine for each of the following expressions:

b. 3x2 + 4x

Square inputMultiply square by 3Add 4 to the product

3x2 + 4

Draw a relationship machine for each of the following expressions:

c. 4x – 3

Draw a relationship machine for each of the following expressions:

c. 4x – 3x

Multiply by 4Subtract 3 from the product

4x – 3

Draw a relationship machine for each of the following expressions:

d. 5x2 + 8

Draw a relationship machine for each of the following expressions:

d. 5x2 + 8x

Square inputMultiply square by 5Add 8 to the product

5x2 + 8

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.

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.

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.

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.

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.

Direction: Write YES if it is an algebraic expression or a polynomial and NO if it is

not.

Given Algebraic Expression Polynomial

1.) 4

2.)

3.) 4x +

4.) twice x

5.)

Direction: Write YES if it is an algebraic expression or a polynomial and NO if it is not. -

Answers

Given Algebraic Expression Polynomial

1.) YES NO

2.) YES NO

3.) 4x + YES YES

4.) twice x NO NO

5.) YES NO