Fundamental Theorem of Algebra

Front

What does the degree of a polynomial indicate about its roots?

Back

The degree of a polynomial indicates the maximum number of roots (or zeros) it can have.

Front

How many zeros does a polynomial of degree n have?

Back

A polynomial of degree n has exactly n roots, counting multiplicities.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when it is expressed as a sum of terms in descending order of their degrees.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial function has at least one complex root.

Front

How can you determine the degree of a polynomial?

Back

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

Front

What is a factor of a polynomial?

Back

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder.

Front

What does it mean if a polynomial has a root at x = r?

Back

If a polynomial has a root at x = r, it means that when x is substituted with r, the polynomial evaluates to zero.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor.

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 equal to f(c).

Front

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

Back

To verify if (x - c) is a factor of a polynomial, evaluate the polynomial at c. If f(c) = 0, then (x - c) is a factor.