Honors Algebra 2 - Ch 4 Lessons 4.1-4.3

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What does it mean if a polynomial has an odd degree?

Back

If a polynomial has an odd degree, it means that the graph of the polynomial will have opposite end behaviors; as x approaches positive infinity, the polynomial approaches positive or negative infinity, and as x approaches negative infinity, it approaches the opposite.

Front

What does it mean if a polynomial has an even degree?

Back

If a polynomial has an even degree, it means that the graph of the polynomial will have the same end behaviors; both ends will either go to positive infinity or negative infinity.

Front

How do you identify the leading coefficient of a polynomial?

Back

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

Front

What is the significance of the leading coefficient's sign?

Back

The sign of the leading coefficient affects the end behavior of the polynomial's graph; a positive leading coefficient means the graph rises to the right, while a negative leading coefficient means it falls to the right.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial, similar to numerical long division.

Front

What is the result of dividing (8x^2 + 6x - 20) by (4x - 5)?

Back

The result is 2x + 4 with a remainder.

Front

What is a remainder in polynomial division?

Back

A remainder is what is left over after dividing one polynomial by another when the division does not result in a whole polynomial.

Front

How can you determine if a polynomial is positive or negative?

Back

You can determine if a polynomial is positive or negative by evaluating it at specific points or analyzing the leading coefficient and degree.

Front

What is the relationship between the degree of a polynomial and the number of roots it can have?

Back

The degree of a polynomial indicates the maximum number of roots (real or complex) it can have.