Polynomials- Classification, Graphs, and Operations

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^2 + 3x + 1 is a polynomial.

Front

What are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

Front

Classify the polynomial 5x^2 + 3x - 7 by degree and number of terms.

Back

Quadratic trinomial (degree 2, 3 terms).

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the values of the polynomial behave as the input approaches positive or negative infinity.

Front

How do you find the difference of two polynomials?

Back

To find the difference, subtract the coefficients of like terms from each polynomial. For example, (3 - 2x + 2x^2) - (4x - 5 + 3x^2) results in -x^2 - 6x + 8.

Front

What is a binomial?

Back

A binomial is a polynomial with exactly two terms. For example, 3x + 4 is a binomial.

Front

What is a cubic polynomial?

Back

A cubic polynomial is a polynomial of degree 3. It can be expressed in the form ax^3 + bx^2 + cx + d.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (FOIL for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 2x^3 + 3x^2 + 1, the leading coefficient is 2.

Front

What is the difference between a monomial and a polynomial?

Back

A monomial is a polynomial with only one term, while a polynomial can have multiple terms. For example, 5x is a monomial, while 5x + 3 is a polynomial.