LT#9: Polynomial Sketching

Front

What is a polynomial?

Back

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

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the Greatest Common Factor (GCF)?

Back

The GCF is the largest polynomial that divides all terms of a polynomial without leaving a remainder.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

Front

What is the multiplicity of a zero?

Back

The multiplicity of a zero refers to the number of times a particular zero appears as a root of the polynomial.

Front

What is the significance of the leading coefficient in a polynomial?

Back

The leading coefficient determines the end behavior of the polynomial's graph and influences its growth as x approaches positive or negative infinity.

Front

What does it mean for a polynomial to have an odd degree?

Back

A polynomial has an odd degree if the highest exponent of its variable is an odd number, which typically results in a graph that has opposite end behaviors.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest exponent of its variable is an even number, which typically results in a graph that has the same end behavior.

Front

How do you determine the number of real zeros of a polynomial?

Back

The number of real zeros can be determined by analyzing the degree of the polynomial and using the Fundamental Theorem of Algebra.

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its linear factors and/or irreducible quadratic factors.