Polynomials (Operations, Classify, End Behavior)

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. It can be expressed in the form: a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

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. It influences the direction of the graph as x approaches positive or negative infinity.

Front

How do you classify polynomials based on their degree?

Back

Polynomials can be classified as follows: 0 degree - constant, 1 degree - linear, 2 degree - quadratic, 3 degree - cubic, 4 degree - quartic, and 5 degree or more - quintic or higher.

Front

What is the degree of the polynomial 4x^3 - 2x^2 + 5?

Back

The degree of the polynomial 4x^3 - 2x^2 + 5 is 3, which is the highest exponent of x.

Front

What is the sum of (2x^2 + 5x - 7) + (3 - 4x^2 + 6x)?

Back

The sum is -2x^2 + 11x - 4.

Front

What is the simplified form of (2x + 5y - z) + (-6x - 4y + 7z)?

Back

The simplified form is -4x + y + 6z.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

What is the end behavior of a polynomial with an odd degree and a positive leading coefficient?

Back

The end behavior of a polynomial with an odd degree and a positive leading coefficient rises to the right and falls to the left.

Front

What is the end behavior of a polynomial with an even degree and a negative leading coefficient?

Back

The end behavior of a polynomial with an even degree and a negative leading coefficient falls to the right and falls to the left.