Ch.5 Test Review

Front

What is a binomial?

Back

A binomial is a polynomial that contains exactly two terms, such as (x - 9).

Front

What does it mean for a binomial to be a factor of a polynomial?

Back

A binomial is a factor of a polynomial if the polynomial can be divided by the binomial without leaving a remainder.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the function equal to zero and solve for the variable.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a binomial of the form (x - c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that if f(c) = 0 for a polynomial f(x), then (x - c) is a factor of f(x).

Front

How do you factor a polynomial completely?

Back

To factor a polynomial completely, find all factors, including any irreducible factors, until no further factoring is possible.

Front

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

Back

A polynomial of degree n can have at most n zeros, counting multiplicities.

Front

What is the significance of complex zeros in polynomial functions?

Back

Complex zeros indicate that the polynomial does not intersect the x-axis at those points, and they occur in conjugate pairs.

Front

What is the process for solving quadratic equations by factoring?

Back

To solve a quadratic equation by factoring, rewrite the equation in standard form, factor it, and then set each factor equal to zero.

Front

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

Back

A polynomial is completely factored when it is expressed as a product of irreducible polynomials over the given number system.