Unit 11: Exponents and Polynomials
commutative property of addition
Two real numbers can be added in any order without changing the sum. For example, 6 + 4 = 4 + 6.
Polynomial
A monomial or the sum or difference of two or more monomials.
factor
A number or mathematical symbol that is multiplied by another number or mathematical symbol to form a product. For example, in the equation 4 • 5 = 20, 4 and 5 are ___________.
term
A number or product of a number and variables raised to powers. 4x, −5y², 6, and x³y⁴ are all examples of ________.
Coefficient
A number that multiplies a variable.
Monomial
A polynomial with exactly one term. 4x, −5y², and 6 are all examples of ____________.
Trinomial
A polynomial with exactly three terms, such as 5y² - 4y + 4 and x² + 2xy +y².
Binomial
A polynomial with exactly two terms, such as 5y² - 4x and x⁵ + 6.
scientific notation
A positive number is written in ______________ if it is written as a x 10ⁿ where the coefficient a has a value such that 1 ≤ a < 10 and n is an integer.
exponential notation
A shorter way to write repeated multiplication. For example, 2⁴ means 2 • 2 • 2 • 2. Two is used as a factor 4 times.
constant
A symbol that represents a quantity that cannot change. It can be a number, letter or a symbol.
quotient rule for exponents
For any non-zero number x and any integers a and b:
associative property of addition
For three or more real numbers, the sum is the same regardless of how you group the numbers. For example, (6 + 2) + 1 = 6 + (2 + 1).
degree of a monomial
The _____________________ is the power to which the variable is raised. For example, the monomial 5y² has a degree of 2. If the monomial contains several variables then the __________________ is the sum of the degree of all the variables. For example, the monomial 7x²y³ has a degree of 5.
like terms
Terms that contain the same variables raised to the same powers. For example, 3x and −8x are _______ _______, as are 8xy² and 0.5xy².
base
The expression that is being raised to a power when using exponential notation. In 5³, 5 is the _______, which is the number that is repeatedly multiplied. 5³ = 5 • 5 • 5. In aᵇ, a is the _______.
degree of a polynomial
The highest exponent or sum of exponents of a term in a polynomial. For example, 7x²y³ + 3x²y − 8 is a 5th degree polynomial because the highest sum of exponents in a term is 2 + 3 = 5.
product raised to a power rule
The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: (ab)ˣ = aˣ • bˣ
degree
The value of an exponent.
product rule for exponents
To multiply two exponential terms with the same base, add their exponents. (xᵃ)(xᵇ) = xᵃ+ᵇ
power rule for exponents
To raise a power to a power, multiply the exponents. (xᵃ)ᵇ = xᵃ*ᵇ
exponent
When a number is expressed in the form aᵇ, ᵇ is the __________. The _________ indicates how many times the base is used as a factor. Power and _________ mean the same thing.
