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# Polynomials

### Vocabulary for Algebra I - Exponents and Polynomials

Zero Exponent Any nonzero number raised to the zero power is 1
Negative Exponent A nonzero number raised to a negative exponent is equal to 1 divided by that number raised to the corresponding positive exponent.
Scientific Notation a method of writing numbers that are very large or very small in two parts - a number between 1 & 10 that is multiplied by ten raised to a positive or negative power
An exponential expression is completely simplified if... 1) there are no negative exponents 2) the same base does not appear more than once in a product or quotient 3) no powers, products or quotients are raised to powers 4) numerical coefficients in a quotient do not have any common factor other than 1
Product of Powers Property The product of two powers with the same base equals that base raised to the sum of the powers
Power of a Power Property A power raised to another power equals that base raised to the product of the exponents
Power of a Product Property A product raised to a power equals the product of each factor raised to that power
Quotient of Powers Property The quotient of two nonzero powers with the same base equals to base raised to the difference of the exponents
Positive Power of a Quotient Property A quotient raised to a positive power equals the quotient of of each base raised to that power
Negative Power of a Quotient Property A quotient raised to a negative power equals the reciprocal of the quotient raised to the opposite (positive) power
Root Index the small number to the left of the radical symbol that tells you which root to take - 2 would be square root, 3 would be cube root, etc.
Factional Exponent 1/n A number raised to the power of 1/n is equal to the "n"th root of that number
Factional Exponent m/n A number raised to the power of m/n is equal to the "n"th root of the number raised to the "m"th power
Monomial A number, a variable or a product of numbers and variables with whole-number exponents
Degree of a Monomial The sum of the exponents of the variables in a monomial
Polynomial A monomial or a sum or difference of monomials
Degree of a Polynomial The degree of the of the term with the greatest degree
Standard Form of a Polynomial Contains one variable and is written in with the terms in order from greatest degree to least degree
Leading Coefficient When written in standard form, it is the coefficient of the first term
Linear Polynomial Polynomial with the degree of 1
Quadratic Polynomial Polynomial with the degree of 2
Cubic Polynomial Polynomial with the degree of 3
Binomial Polynomial with two terms
Trinomial A polynomial with three terms
FOIL A method for multiplying binomials: F - multiply first terms O - multiply outside terms I - multiply inside terms L - multiply last terms
Perfect Square Trinomial A trinomial that results from squaring a binomial
Created by: gklee