Chapter 7: Polynomials

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# Chapter 7: Polynomials - PowerPoint PPT Presentation

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

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

• Here are the concepts that need to be reviewed before starting Chapter 7:
• Represent expressions using algebra tiles.
• The zero principle
• Polynomials
• Factors
• A term is an expression formed by the product of numbers and variables.
• 3x2 et 4x are examples of terms.
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.
There are 2 parts of a term:

The numerical coefficient

The literal coefficient

The parts of a term
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 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 is an algebraic expression consisting of one or more terms separated by addition (+) or subtraction (-) symbols.
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 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 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
• 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
• When you apply the distributive property, you are expanding an expression.

Area models using Alge-Tiles.

F.O.I.L.

7.4: Multiply two binomials
The area of a rectangle

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

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.)
• 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
• When you multiply 2 binomials together, you will get a trinomial ***
• For example:
• (x + 2)(x + 3) = x2 + 5x + 6
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)
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
• 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?
• 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
• 3x + 12 = 3(x + 4)
• 3x + 12 = 3(x + 4) are equivalent expressions.
The expanded form
• 3x + 12 is in the expanded form and contains two terms.
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
• 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.