LT#9: Polynomial Sketching

Front

What does multiplicity of a zero mean?

Back

Multiplicity of a zero refers to how many times a particular zero (or root) of a polynomial equation is repeated.

Front

Which of the following could be the equation of the graph in factored form? y=-(x+1)(x-2)(x-4), y=(x+1)²(x-2)(x-4)³, y=x(x+1)(x-2)(x-4), y=(x+1)³(x-3)(x-1)²

Back

y=-(x+1)(x-2)(x-4) is a valid equation in factored form.

Front

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

Back

If a polynomial function has an odd degree, it means that the graph will have opposite end behaviors, typically going from the bottom left to the top right.

Front

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

Back

If a polynomial function has an even degree, it means that the graph will have the same end behavior, typically going from the top left to the top right or bottom left to bottom right.

Front

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

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 leading coefficient of a polynomial?

Back

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

Front

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

Back

The sign of the leading coefficient determines the end behavior of the polynomial graph.

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, first find the greatest common factor (GCF), then factor the remaining polynomial using techniques such as grouping or applying special products.

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.

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x that makes the function equal to zero.