Polynomials Flashcards
What is algebra?
Branch of mathematics that uses symbols to represent unknown numbers
Algebra forms the foundation for many areas of mathematics.
Define expression in mathematics.
Collection of numbers, operations, and symbols
Expressions do not contain equality or inequality signs.
What is an equation?
Statement that two mathematical expressions have the same value
Equations often include variables and constants.
What is an inequality?
Statement comparing expressions that might not be equal
Inequalities use symbols like >, <, ≥, and ≤.
What is a coefficient?
Number multiplying a variable
Coefficients can be integers, fractions, or decimals.
What is a variable?
Symbol used to represent a number
Variables are often denoted by letters such as x, y, or z.
What is a constant in mathematics?
Numerical part of an expression
Constants have fixed values and do not change.
What characterizes a non-polynomial?
Contains negative exponent, variable as a denominator, or variable under square root
These features disqualify an expression from being a polynomial.
What is a polynomial?
An algebraic expression formed by adding or subtracting terms
Polynomials can include constants, variables, and non-negative integer exponents.
How is the degree of a term determined?
By the exponent values of each term
The degree is the highest exponent in that term.
How is the degree of a polynomial determined?
By finding the degree of the highest term
The degree indicates the polynomial’s highest power.
What does standard form mean in relation to polynomials?
To write a polynomial in order of the highest degree terms
Standard form arranges terms from largest to smallest exponent.
What is the degree of a polynomial?
The largest exponent
The degree indicates the highest power of the variable in the polynomial.
How are terms in a polynomial arranged in standard form?
From largest to smallest exponent
This arrangement helps in identifying the leading term easily.
What are the parts of a polynomial called?
Terms
Terms are the individual components that are added or subtracted together.
What is the leading coefficient?
The first coefficient
It is the coefficient of the term with the highest degree.
What is a constant in a polynomial?
A term that has no variable
Constants are independent of any variable and remain the same.
Define a monomial.
A polynomial with 1 term
Examples include 5x or 3y^2.
Define a binomial.
A polynomial with 2 terms
Examples include x + 3 or 2y - 5.
Define a trinomial.
A polynomial with 3 terms
Examples include x^2 + 2x + 1.
What is a polynomial?
A polynomial with 4 or more terms
Examples include x^3 + x^2 + x + 1.
What do algebra tiles help understand?
Polynomial addition and subtraction
Algebra tiles visually represent polynomials and their operations.
What does the legend on algebra tiles identify?
If a block is negative or positive
This helps in visualizing the addition or subtraction of polynomials.
Fill in the blank: A _______ has 1 term.
Monomial
Fill in the blank: A _______ has 2 terms.
Binomial
Fill in the blank: A _______ has 3 terms.
Trinomial
True or False: A polynomial can have any number of terms.
True
A polynomial is defined as having 4 or more terms.
