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

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chapter 7 polynomials

Chapter 7: Polynomials

This chapter starts on page 320, with a list of key words and concepts.

chapter 7 get ready
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
7 1 add and subtract polynomials
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.
what is a variable
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.
the parts of a term
There are 2 parts of a term:

The numerical coefficient

The literal coefficient

The parts of a term
the numerical coefficient
The numerical coefficient
  • The numeric factor of a term is called the numerical coefficient.
  • For example, the numerical coefficient of 4x is 4.
the literal coefficient
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.
a polynomial
A polynomial
  • A polynomial is an algebraic expression consisting of one or more terms separated by addition (+) or subtraction (-) symbols.
the definition of each polynomial
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.
like terms
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.
an algebraic model
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.
7 3 multiply a monomial by a polynomial
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
the expansion of expressions
The expansion of expressions
  • When you apply the distributive property, you are expanding an expression.
the area of a rectangle
The area of a rectangle

Area of a rectangle = length of rectangle x width of rectangle

method 1 area models
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.
method 2 f o i l
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.
the result of multiplying 2 binomials
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
7 5 polynomial division
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)
7 2 common factors
There are 3 ways to factor a polynomial:

The sharing model

The area model

The greatest common factor method

7.2: Common Factors
factoring a polynomial
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.
which method should you use
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.
an example of factoring
An example of factoring
  • 3x + 12 = 3(x + 4)
  • 3x + 12 = 3(x + 4) are equivalent expressions.
the expanded form
The expanded form
  • 3x + 12 is in the expanded form and contains two terms.
the factored form
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.
7 6 applying algebraic modeling
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.
the summary of chapter 7
The summary of Chapter 7
  • What did we learn about in this chapter?