*AA C&C Unit 4 Test REVIEW Part 1

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial evaluates to zero. They are also known as the roots of the polynomial.

Front

How do you find the equation of a polynomial given its zeros?

Back

To find the equation of a polynomial given its zeros, you can use the fact that if r1, r2, ..., rn are the zeros, the polynomial can be expressed as p(x) = k(x - r1)(x - r2)...(x - rn), where k is a constant.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial. It determines the polynomial's end behavior and the maximum number of zeros it can have.

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity.

Front

What does it mean for a polynomial to have a degree of 5?

Back

A polynomial of degree 5 can have up to 5 real roots and will have a maximum of 4 turning points.

Front

How do you determine the number of real solutions of a quadratic equation using the discriminant?

Back

The discriminant (D) is calculated as D = b^2 - 4ac. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

What is the discriminant of the quadratic equation -2x^2 - x + 1 = 0?

Back

The discriminant is 9.

Front

What is the relationship between the multiplicity of a root and the graph of a polynomial?

Back

The multiplicity of a root indicates how many times that root appears in the factorization of the polynomial. A root with odd multiplicity will cross the x-axis, while a root with even multiplicity will touch the x-axis and turn around.

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, which correspond to its zeros.

Front

How can you identify the end behavior of a polynomial function from its leading coefficient and degree?

Back

If the leading coefficient is positive and the degree is even, the ends of the graph will rise. If the leading coefficient is negative and the degree is even, the ends will fall. If the degree is odd, the ends will go in opposite directions depending on the sign of the leading coefficient.