Chapter 7: Polynomials

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Transcript Chapter 7: Polynomials

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:
1. Represent expressions using
algebra tiles.
2. The zero principle
3. Polynomials
4. Factors

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?


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:
1.
2.
The numerical
coefficient
The literal
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 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.
Types of polynomials

There are 4
different types of
polynomials:

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Monomials
Binomials
Trinomials
Polynomials
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

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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.
7.4: Multiply two binomials

In order to multiply
2 binomials, there
are 2 methods we
can use:
1.
2.
Area models using
Alge-Tiles.
F.O.I.L.
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:
1. Begin at the bottom left corner with
x2 tiles first.
2. Construct a rectangle in the top right
corner with unit tiles.
3. Fill the top left and bottom right
spaces with x-tiles.

Method #2 (F.O.I.L.)

1.
2.
3.
4.
5.
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
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When you multiply 2 binomials
together, you will get a trinomial ***
For example:
(x + 2)(x + 3) = x2 + 5x + 6
7.5: Polynomial Division
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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:
1.
2.
3.
The sharing model
The area model
The greatest
common factor
method
Factoring a polynomial
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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?
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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
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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
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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
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1.
2.
3.
4.
5.
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

What did we learn about in this
chapter?