Alg 2 - Zeros vs. Factors

Front

What is the definition of a zero of a polynomial?

Back

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

Front

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

Back

The zeros of a polynomial correspond to the values of x that make the polynomial equal to zero, and each zero can be expressed as a factor in the form (x - zero).

Front

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

Back

To find the x-intercepts of a quadratic function, set the function equal to zero and solve for x.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

What is the factored form of a quadratic equation?

Back

The factored form of a quadratic equation is expressed as (x - r1)(x - r2) = 0, where r1 and r2 are the roots or zeros of the equation.

Front

How do you convert from standard form to factored form?

Back

To convert from standard form to factored form, you can factor the quadratic expression or use the quadratic formula to find the roots.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the zeros of a quadratic equation.

Front

What does it mean if a polynomial has a repeated zero?

Back

A repeated zero means that the factor corresponding to that zero appears more than once in the factored form of the polynomial.

Front

How can you determine the number of real zeros a polynomial has?

Back

You can determine the number of real zeros by analyzing the discriminant (b² - 4ac) of the polynomial or by using graphing techniques.

Front

What is the significance of the x-intercepts in a graph of a polynomial function?

Back

The x-intercepts represent the points where the graph crosses the x-axis, indicating the zeros of the function.