Solving Higher Order Polynomials

Front

What is the multiplicity of roots in polynomial equations?

Back

Multiplicity of roots refers to the number of times a particular root appears in the solution set.

Front

Solve the polynomial equation: 0 = x^3 - 3x^2 - 5x + 15

Back

The solutions are 3, √5, -√5.

Front

What can be said about the degree of a polynomial function with an odd degree?

Back

The function has an odd degree.

Front

What is synthetic division used for in polynomial equations?

Back

Synthetic division simplifies the process of dividing higher order polynomials by linear factors.

Front

What are the solutions for the polynomial equation: 0 = 3 (x + 4) (x + 1) (x - 3)?

Back

The solutions are -4, -1, 3.

Front

Define a polynomial function.

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial expression.

Front

Explain the concept of real zeros of a polynomial.

Back

Real zeros of a polynomial are the values of the variable that make the polynomial equal to zero.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How does the end behavior of a polynomial function relate to its degree and leading coefficient?

Back

The end behavior of a polynomial function is determined by its degree and leading coefficient; odd degree with positive leading coefficient goes up to the right and down to the left.