Fundamental Theorem of Algebra

Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial equation of degree n has exactly n complex roots, counting multiplicities.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

If a polynomial has a complex zero, what can be said about its conjugate?

Back

The conjugate of a complex zero is also a zero of the polynomial.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is determined by the largest exponent of its variable.

Front

What is the relationship between the degree of a polynomial and the number of zeros?

Back

The degree of a polynomial indicates the maximum number of zeros it can have.

Front

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

Back

The leading coefficient affects the end behavior of the polynomial graph.

Front

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

Back

A polynomial is factored completely when it is expressed as a product of irreducible polynomials.

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by (x - c) is f(c).

Front

How can you verify if (x - c) is a factor of a polynomial?

Back

If f(c) = 0, then (x - c) is a factor of the polynomial f(x).