1. Chapter 7: Polynomials
This chapter starts on page 320, with a list of key words and concepts.

2. Chapter 7: Get Ready!
Here are the concepts that need to be reviewed before starting Chapter 7:
Represent expressions using algebra tiles.
The zero principle
Polynomials
Factors

3. 7.1 Add and Subtract Polynomials!
A term is an expression formed by the product of numbers and variables.
3x2 et 4x are examples of terms.

4. What is a variable?
A variable is a letter that is used to represent a value that can change or vary.
For example, in 4x – 1, the variable is x.

5. The parts of a term The numerical coefficient The literal coefficient
There are 2 parts of a term:
The numerical coefficient
The literal coefficient

6. The numerical coefficient
The numeric factor of a term is called the numerical coefficient.
For example, the numerical coefficient of 4x is 4.

7. The literal coefficient
The non-numeric factor (i.e. the letter) of a term is called the literal coefficient.
For example, the literal coefficient of 4x is x.

8. A polynomial
A polynomial is an algebraic expression consisting of one or more terms separated by addition (+) or subtraction (-) symbols.

9. Types of polynomials There are 4 different types of polynomials:
Monomials
Binomials
Trinomials
Polynomials

10. The definition of each polynomial
A monomial has one term.
A binomial has two terms.
A trinomial has three terms.
A polynomial is an expression having 4 terms or more.

11. Like terms
Like terms are terms that have the same literal coefficient.
For example, 3x et 4x are like terms because they have the same literal coefficient, x.

12. An algebraic model
An algebraic model can represent a pattern, a relationship or a numeral sequence.
An algebraic model is always written in the form of an algebraic expression, algebraic equation or algebraic formula.

13. 7.3: Multiply a monomial by a polynomial
Here is the distributive property, a rule that allows you to simplify expressions involving the multiplication of a monomial by a polynomial.
3(x + 2) = 3(x) + 3(2) = 3x + 6

14. The expansion of expressions
When you apply the distributive property, you are expanding an expression.

15. 7.4: Multiply two binomials
In order to multiply 2 binomials, there are 2 methods we can use:
Area models using Alge-Tiles.
F.O.I.L.

16. The area of a rectangle
Area of a rectangle = length of rectangle x width of rectangle

17. Method #1 (Area models)
When building rectangular tile models, use these directions:
Begin at the bottom left corner with x2 tiles first.
Construct a rectangle in the top right corner with unit tiles.
Fill the top left and bottom right spaces with x-tiles.

18. Method #2 (F.O.I.L.)
In order to use the F.O.I.L. method properly, use these directions:
The F: multiply the 2 first terms together
The O: multiply the 2 outer terms together
The I: multiply the 2 interior terms together
The L: multiply the 2 last terms together
Add all the products together in order to obtain the simplified expression.

19. The result of multiplying 2 binomials
When you multiply 2 binomials together, you will get a trinomial ***
For example:
(x + 2)(x + 3) = x2 + 5x + 6

20. 7.5: Polynomial Division
To divide a polynomial by a monomial, it is like applying the distributive property in reverse.
For example, (6x + 9) ÷ 3 = (6x/3) + (9/3) = 2x + 3
*** A number divided by itself equals 1. (4÷4=1 et x÷x=1)

21. 7.2: Common Factors There are 3 ways to factor a polynomial:
The sharing model
The area model
The greatest common factor method

22. Factoring a polynomial
In order to factor a polynomial completely, find the polynomial’s greatest common factor.
You can find these common factors in the numerical coefficients, in the literal coefficients or in the both of them.

23. Which method should you use?
The sharing model works best when the common factor is a number.
The area model works best when the common factor is a letter.

24. An example of factoring
3x + 12 = 3(x + 4)
3x + 12 = 3(x + 4) are equivalent expressions.

25. The expanded form
3x + 12 is in the expanded form and contains two terms.

26. The factored form 3(x + 4) is in the factored form.
The factored form has 2 types of factors: 3 is the common numeric factor and (x + 4) is the polynomial factor.

27. 7.6: Applying algebraic modeling
Here is how you can solve an algebraic word problem:
Read the problem at least 3 times.
Identify the known and unknown quantities.
Make a plan that will solve for the unknown quantities.
Solve your problem with the plan that you came up with in #3.
Write your final answer in a complete sentence.

28. The summary of Chapter 7
What did we learn about in this chapter?