Quarter 2 Exam Review

Front

What is the degree of a polynomial function?

Back

The degree of a polynomial function is the highest power of the variable in the polynomial. For example, in P(x) = 3x^4 + 4x - 8, the degree is 4.

Front

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

Back

The number of zeros of a polynomial function is equal to its degree. For example, a polynomial of degree 4 can have up to 4 zeros.

Front

What does it mean for a root to have multiplicity?

Back

A root has multiplicity if it is a solution to the polynomial equation more than once. For example, in f(x) = (x+2)(x-3)^2(x-4), the root 3 has a multiplicity of 2.

Front

What is an extremum in the context of a graph?

Back

An extremum is a point on a graph where the function reaches a local maximum or minimum. The number of extrema can be determined by analyzing the graph's turning points.

Front

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

Back

The leading term of a polynomial determines the end behavior of the graph. For example, if the leading term has a negative coefficient and an even degree, the graph will fall on both ends.

Front

How do you find the roots of a cubic equation?

Back

To find the roots of a cubic equation, you can use factoring, synthetic division, or the Rational Root Theorem, and for complex roots, apply the quadratic formula.

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution of a polynomial equation is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

What is the difference between even and odd degree polynomials?

Back

Even degree polynomials have the same end behavior on both sides (both up or both down), while odd degree polynomials have opposite end behavior (one side up, the other down).

Front

What does it mean for a polynomial to have complex roots?

Back

Complex roots occur in conjugate pairs and are solutions to polynomial equations that cannot be factored into real numbers. For example, x = 2 ± 2i√5 are complex roots.

Front

How can you determine the number of extrema from a polynomial's degree?

Back

A polynomial of degree n can have at most n-1 extrema. For example, a polynomial of degree 4 can have up to 3 extrema.