Classifying Polynomials

What is a polynomial?

• A mathematical expression consisting of variables, coefficients, and non-negative integer exponents, combined using addition, subtraction, and multiplication.

• A type of equation that only includes variables and constants without any operations.

• A mathematical expression that can only include positive integers and no variables.

• A formula used to calculate the area of geometric shapes.

How are polynomials classified by the number of terms?

• Monomials (1 term), binomials (2 terms), trinomials (3 terms), or polynomials with more than three terms.

• Only monomials and binomials are considered polynomials.

• Polynomials are classified based on their degree only.

• Polynomials can only be classified as monomials or trinomials.

What is a monomial?

• A polynomial with only one term.

• A polynomial with two terms.

• A polynomial with three or more terms.

• A constant value that does not change.

What is the standard form of a polynomial?

• The standard form of a polynomial is when the terms are arranged in ascending order of their degrees.

• The standard form of a polynomial is when the terms are arranged in descending order of their degrees.

• The standard form of a polynomial is when all coefficients are equal to one.

• The standard form of a polynomial is when the polynomial is factored completely.

How are polynomials classified by degree?

• By their highest degree: constant (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3)

• By their coefficients: positive, negative, or zero

• By their number of terms: monomial, binomial, or trinomial

• By their variable: single variable or multiple variables

What is a binomial?

• A polynomial with exactly one term.

• A polynomial with exactly two terms.

• A polynomial with three or more terms.

• A type of irrational number.

Can a polynomial have a negative coefficient?

• No, a polynomial cannot have negative coefficients.

• Yes, a polynomial can have negative coefficients, as long as the exponents of the variables are non-negative integers.

• Only if the polynomial is of degree zero.

• Yes, but only in certain mathematical contexts.

What is a quadratic polynomial?

• A polynomial of degree 1

• A polynomial of degree 2, which can be expressed in the form ax² + bx + c.

• A polynomial of degree 3

• A constant polynomial that does not change value.

What is the difference between a polynomial and a non-polynomial expression?

• A polynomial consists of non-negative integer exponents, while non-polynomial expressions may include negative exponents, fractional exponents, or variables in the denominator.

• A polynomial can only have positive integer coefficients, while non-polynomial expressions can have any type of coefficients.

• A polynomial is always a single term, while non-polynomial expressions can have multiple terms.

• A polynomial must have at least one variable, while non-polynomial expressions can be constant numbers.

What is a cubic polynomial?

• A polynomial of degree 2

• A polynomial of degree 3, expressed as ax³ + bx² + cx + d

• A polynomial of degree 4

• A linear polynomial expressed as ax + b