Algebra 1 Terms Flashcards
What is a real number?
numbers that are made of rational and irrational #’s
What is a signed number?
numbers that are positive, negative, or zero.
What is a real number?
A number that can be expressed as a quotient of an integer divided by a nonzero integer or a decimal that terminates or repeats. (Can turn into fraction)
For example: 1, 5, 9.67, ⅓ etc.
What is an irrational number?
Number that can’t be expressed as the quotient of 2 integers. Decimals don’t terminate or repeat. (Can’t be turned into a fraction)
For example: 7.87903.., √6, 5.4783…, 𝜋
What is a rational root?
numbers to the perfect nth power
For example : √4, √36, -√16
What is an irrational root?
non perfect squares
For example: √2, √7, 2*√5
What is an exponent?
A small raised number written to the upper right of a quantity called the base for the exponent.
The exponent how many times to use the base as a factor
What is the base of an exponential expression?
X is the base
What is a polynomial?
a single monomial or the (algebraic) sum of two or more monomials.
What is a monomial?
A single term that is the product of a constant and one or more variables with nonnegative integer exponents
What is a binomial?
a polynomial with exactly two terms
What is a trinomial?
a polynomial with exactly three terms
What is the numerical coefficient?
The number part of a monomial
For example: 3x
Numerical coefficient = 3
What is the degree of a monomial?
The sum of the exponents of the variables in a monomial
What is the leading term in a polynomial?
The term with the variable with the greatest power
What is the leading coefficient in a polynomial?
The coefficient in the leading term
What is a constant term in a polynomial?
The last term
What is the special product of perfect squares?
(x+y)^2 = x^2 + 2xy + y^2
(x-y)^2 = x^2 - 2xy + y^2
What is the special product of, “the difference of two squares?”
(x+y)(x-y) = x^2 - y^2
What is the special product of perfect cubes?
(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
(x-y)^3 = x^3 - 3x^2y +3xy^2 - y^3
What is the special product of, “the sum of two cubes?”
(x+y)(x^2-xy+y^2) = x^3+y^3
What is the special product of, “the difference of two cubes”
(x-y)(x^2+xy+y^2) = x^3-y^3
What is a rational expression?
an algebraic expression that can be written as the ratio of two polynomials. The denominator in a rational expression can’t be equal to zero since division by 0 is undefined.
What does the Fundamental Principle of Rational Expressions Allow you to do with polynomials?
It allows you to reduce rational expressions to lowest terms by dividing the numerator and to denominator by the GCF
