S1 Final exam Review Units 3 and 4

Front

What is the factored form of the polynomial 3x^4 + 3x^3 - 12x^2 - 12x?

Back

3x(x+2)(x-2)(x+1)

Front

What are the possible types of solutions for a polynomial of degree 4?

Back

4 real OR 4 complex OR 2 real and 2 complex

Front

What is the factored form of the polynomial represented by the graph f(x)?

Back

f(x) = (x+4)(x+1)^2(x-2)(x-4)

Front

How do you find the vertical asymptote of a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

Which polynomial is factored entirely into linear factors?

Back

f(x) = (x^2-4)(x-2)(x+3)

Front

What is the definition of a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity.

Front

What does it mean for a polynomial to be factored completely?

Back

It means that the polynomial is expressed as a product of irreducible factors, typically linear factors.

Front

What is the significance of the degree of a polynomial?

Back

The degree indicates the highest power of the variable and determines the polynomial's behavior and number of roots.

Front

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

Back

Use the Fundamental Theorem of Algebra and analyze the polynomial's degree and discriminant.

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree determines whether the ends of the graph rise or fall as x approaches positive or negative infinity.