7-1 Adding and Subtracting Polynomials Flashcards
What is a monomial?
A term composed of:
a positive or a negative sign
a number
variable(s)
(number)(one or more variables)
What would keep a term from being a monomial?
a variable in the denominator of a fraction
radical symbols
fraction exponents
negative exponents
How do you determine the degree of a monomial?
Add the exponents of all the variables.
(Remember to write a 1 as exponent for any variable that does not have a variable)
What is the degree of a constant?
0
5 can be written as (5)(1) and (5)(1) can be written as (5)(x^0).
The variable we do not see beside any constant has an exponent of 0.
What is a polynomial?
a monomial or the sum or difference of two or more monomials
How do you determine the degree of a polynomial?
Find the degree of each monomial by adding the exponents of its variables.
The degree will be the highest sum.
How are polynomials classified by their degree?
0 - constant
1 - linear
2 - quadratic
3 - cubic
4 - 4th degree
How are polynomials classified by the number of terms!
1 - monomial
2 - binomial
3 - trinimial
What are the two ways a polynomial can be classified?
By their degree and by the number of terms
How do you write a polynomial in standard form?
Rearrange the terms so that the exponents are from largest to smallest.
The constant term is always listed last.
How do you add polynomials?
Find terms with the exact same variable and exponent. Combine their coefficients and keep the same variable and exponent.
Comtinue until all like terms have been combined. Then rewrite in standard form.
How do you subtract polynomials?
Find terms with the exact same variable and exponent. First coefficient minus second coefficient; keep the same variable and exponent.
Comtinue until all like terms have been combined. Then rewrite in standard form.
What does the Closure Property say about adding polynomials?
polynomial + polynomial = polynomial
When adding two polynomials, the result will always be a polynomial.
What does the Closure Property say about Subtracting polynomials?
polynomial - polynomial = polynomial
When subtracting two polynomials, the result will always be a polynomial.
