Day 6: Communicate with Algebra
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Review the Divisibility Rules on the other handout
Do the examples
Algebra Terminology
Definitions
Term:
an expression formed by the product of numbers and/or variables
A term could be:
- a number (constant)
- the product of one or more variables
3x
Numerical coefficient
- the product of a number and one or more variables
Variable
Coefficient:
also called the numerical coefficient, it is the number in a term
Variable:
consists of one or more variables and their exponents, if they exist
The expression, -7x2, is a __________ where the coefficient is ______ and the variable is _____.
Constant:
a term that contains no variable, its value does not change
Any number is a constant!
Polynomial: An algebraic expression consisting of one or more terms connected by addition
or subtraction.
Illustration:
2x 3  5x 2  7, 3a  4b
Note: The terms of a polynomial are usually written in descending order of exponents.
Illustration:
 4x3  5x2  2x  6
3
2
not 2x  6  4x  5x
A polynomial can be classified by the number of terms:
Monomial:
Binomial:
Trinomial:
a polynomial with only one term.
A polynomial with two terms separated by a “+” or “-“sign.
A polynomial with three terms separated by “+” or “-“signs.
Number of terms
Name of Polynomial
Example
1 term
2x
2 terms
2x – 3y
3 terms
2x – 3y + 5
4 or more terms
3x3 – 4x2 + 9x - 5
Degree of a term:
the sum of the exponents on the variables in a term.
Degree of a polynomial:
the highest degree of the terms in the polynomial
A polynomial can be classified by the degree:
Degree
Name of Polynomial
Example
0
4
1
x
2
x2 – 3x
3
2x3 – x2 + 4x - 1
4
-7x4 + 3x + 5
5
x5 – 2x4 + 7x3 + 3x2 – 5x + 13
6 or more
9x7 + 2x5 + 3x2 + 6
Example 1:
Complete the table.
Polynomial
3x 2 y  2xy 
Number
of terms
Classify Polynomial
by number of
terms
Degree of
polynomial
Classify Polynomial
by Degree
5
2
3x 5
6x 5 y 3z2
129a3b  12.5b
Consolidation:
1. Fill in the blanks.
Surface Area: 2πr2 +2πrh
The first term has a degree of_____, the second term has a degree
of_____. The highest degree is _____, therefore the degree of the
expression is _____.
This makes sense because area is ____-dimensional.
This Polynomial is a ____________________ because it has ______
terms.
Surface Area: πrs + πr2
The first term has a degree of_____, the second term has a degree
of_____. The highest degree is _____, therefore the degree of the
expression is _____.
This makes sense because area is ____-dimensional.
The ___________________ of both terms is π.
Volume:
1 2
r h
3
The term has a degree of_____, therefore the degree of the expression
is _____.
This makes sense because volume is _____ -dimensional.
This polynomial is a ____________________ because it has ______
terms.
2. Complete the table by identifying the degree of each polynomial.
Polynomial
3x2y – 2xy + 5
-6x3 + 12x2y3 - 16
23.7x5y3 – 2x4y6 – 12.5x7
Term with highest
degree
Degree of polynomial