Synthetic Division and Zeros, Roots, Factors

Front

What is synthetic division?

Back

A method used to divide a polynomial by a linear factor of the form (x - c) without using long division.

Front

What are the roots of a polynomial?

Back

The values of x that make the polynomial equal to zero.

Front

How do you find the x-intercepts of a function?

Back

Set the function equal to zero and solve for x.

Front

What is the relationship between roots and factors of a polynomial?

Back

If r is a root of the polynomial, then (x - r) is a factor of that polynomial.

Front

What is a zero placeholder in synthetic division?

Back

A zero placeholder is used to represent missing terms in a polynomial when performing synthetic division.

Front

How do you determine the degree of a polynomial?

Back

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

Front

What is the remainder theorem?

Back

If a polynomial f(x) is divided by (x - c), the remainder is f(c).

Front

What is the factor theorem?

Back

A polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

Front

How do you graph a polynomial function?

Back

Identify the roots, determine the end behavior, and plot key points to sketch the graph.

Front

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

Back

The leading coefficient determines the end behavior of the polynomial function.