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Concept Map 4.1 - 4.6 María Paula…
Concept Map 4.1 - 4.6 María Paula Bolívar
Algebraic Expressions
Polynomials
Monomials
Definition
An expression that is either a numeral, a variable, or a product of a numeral and one or more variables
Example
7, h, -8xy
Constant
Definition
A numeral
Example
6, 32, 893
Degrees
Of a Monomial in a Variable
Definition
Total number of times it’s variables occur as factors
Example
-3xy^2z^3: 1 in x
2 in y
3 in z
Of a Monomial
Definition
The number of times that variable occurs as a factor in the monomial
Example
-3xy^2z^3: 1+2+3=6
Exponents
Example
3^n
3 is the
base
n is the
exponent
Factored Form
Example
(3)(3)(3)
Exponential Form
Example
3^3
Rules of Exponents
For Multiplication
Definition
When you multiply two powers having the same base, you add the exponents
Example
a^m * a^n = a^m+n
For a Power of a Power
Definition
To find a power of a power, you multiply the exponents
Example
(a^m)^n = a^m*n
For a Power of a Product
Definition
To find a power of a product, you find the power of each factor and then multiply
Example
(ab)^m = a^m b^m
Binomials
Definition
Two terms
Example
4x+9
Trinomials
Definition
Three terms
Example
5b^2+3ab+a^2
Definition
A sum of monomials
Example
x^2-3x-2
Like Terms
Definition
Monomials that are exactly alike or differ only in their coefficient
Example
8x^2y, 5yx^2
Simplified Polynomials
Definition
When no two of it’s terms are similar
Example
-4x^3+5x^2+3x^2+4x^3 = 8x^2
Degree of a Polynomial
Definition
The greatest of the degrees of it’s terms after it has been simplified
Example
(8x^2)-7: degree is 2
Example
(4n+2)(6-5n+4n^2)
simplified
Order of Operations
Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction
Distributive Property
Example
3(-2+7) = (3 x -2)+(3 x 7)
Fractions
Algebraic Equations
Example
(x-3)(x+2)=(x+1)(x+5)
solved