Mod. 7 Review
07.10 Module Seven Review and Practice Test
In this module, you learned about polynomials and how to perform various operations on them. This is your opportunity to review all of the concepts from this module to prepare for your Discussion Based Assessment and Module 7 Test.
Introduction to Polynomials: Lesson 07.01
Polynomials are a specific type of mathematical expression that have: * one or more terms * variables with only positive whole number exponents * no variables in the denominators of each term
Polynomials are classified based on the number of terms and the degree. * -------------------------------------------------
Degree
* A Monomial is a polynomial with one term.
Examples: 5x2y; –8x; 16 * A Binomial is a polynomial with two terms connected by + or – signs.
Examples: 7x + 10; –3x7 – 5xy2 * A Trinomial is a polynomial with three terms connected by + or – signs.
Examples: 5x3 + 2x – 1; –7a + 2ab – 8b * Any polynomial with more than three terms is simply classified as a polynomial.
Example: x3 – 2x2y + 7xy2 – 8y3 (this has 4 terms) * The degree of a term is the sum of the exponents of the variables in the term.
Example: The degree of x2y3 is 2 + 3 = 5. * The degree of a polynomial is equal to the degree of the term with the highest degree.
Example: 8x5y2 + 2x3y6; The degree of 8x5y2 is 5+2 = 7. The degree of 2x3y6is 3+6 = 9. So the degree of the polynomial is 9. * The degree of a constant is zero.
Example: The constant 5 has no variable part. This term could be written as
5x0 which equals 5(1) = 5. Therefore, the degree of this term is zero.
The standard form of a polynomial is when the polynomial is listed with each term in decreasing order of degree. Look at the following examples of polynomials written in standard form.
07.10 Module Seven Review and Practice Test
Addition and Subtraction of Polynomials: Lesson 07.02
To add or subtract polynomial expressions, you must combine like terms. Like
In this module, you learned about polynomials and how to perform various operations on them. This is your opportunity to review all of the concepts from this module to prepare for your Discussion Based Assessment and Module 7 Test.
Introduction to Polynomials: Lesson 07.01
Polynomials are a specific type of mathematical expression that have: * one or more terms * variables with only positive whole number exponents * no variables in the denominators of each term
Polynomials are classified based on the number of terms and the degree. * -------------------------------------------------
Degree
* A Monomial is a polynomial with one term.
Examples: 5x2y; –8x; 16 * A Binomial is a polynomial with two terms connected by + or – signs.
Examples: 7x + 10; –3x7 – 5xy2 * A Trinomial is a polynomial with three terms connected by + or – signs.
Examples: 5x3 + 2x – 1; –7a + 2ab – 8b * Any polynomial with more than three terms is simply classified as a polynomial.
Example: x3 – 2x2y + 7xy2 – 8y3 (this has 4 terms) * The degree of a term is the sum of the exponents of the variables in the term.
Example: The degree of x2y3 is 2 + 3 = 5. * The degree of a polynomial is equal to the degree of the term with the highest degree.
Example: 8x5y2 + 2x3y6; The degree of 8x5y2 is 5+2 = 7. The degree of 2x3y6is 3+6 = 9. So the degree of the polynomial is 9. * The degree of a constant is zero.
Example: The constant 5 has no variable part. This term could be written as
5x0 which equals 5(1) = 5. Therefore, the degree of this term is zero.
The standard form of a polynomial is when the polynomial is listed with each term in decreasing order of degree. Look at the following examples of polynomials written in standard form.
07.10 Module Seven Review and Practice Test
Addition and Subtraction of Polynomials: Lesson 07.02
To add or subtract polynomial expressions, you must combine like terms. Like