Graphing polynomials in factored form

Front

What is the factored form of a polynomial?

Back

The factored form of a polynomial expresses it as a product of its factors, which can be linear or quadratic expressions.

Front

What are the zeros of a polynomial?

Back

The zeros of a polynomial are the values of x for which the polynomial equals zero. They can be found by setting the polynomial equal to zero and solving for x.

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 expression.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree and indicates the direction of the graph as x approaches infinity.

Front

What is the significance of the multiplicity of a zero?

Back

The multiplicity of a zero indicates how many times that zero is repeated in the factored form of the polynomial, affecting the graph's behavior at that zero.

Front

How do you find the factored form of a polynomial given its zeros?

Back

If the zeros of a polynomial are known, the factored form can be constructed by creating factors of the form (x - zero) for each zero.

Front

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

Back

A polynomial of degree n can have up to n zeros, counting multiplicities.

Front

What is the process for graphing a polynomial in factored form?

Back

To graph a polynomial in factored form, identify the zeros, determine the multiplicity, evaluate the leading coefficient, and plot key points.

Front

What is the difference between a linear factor and a quadratic factor?

Back

A linear factor is of the form (x - a), while a quadratic factor is of the form (ax^2 + bx + c). Linear factors have degree 1, and quadratic factors have degree 2.

Front

How can you verify if a polynomial is factored correctly?

Back

You can verify by expanding the factors to see if you obtain the original polynomial.