Final Review -3

Front

What are linear factors?

Back

Linear factors are expressions of the form (x - a), where 'a' is a root of the polynomial. They represent the x-intercepts of the polynomial.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for x. The solutions are the x-values where the graph intersects the x-axis.

Front

What is synthetic division?

Back

Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x - c). It is faster than long division and is used to find the quotient and remainder.

Front

What is the vertex form of a quadratic equation?

Back

Front

What are x-intercepts?

Back

X-intercepts are points where the graph of a function crosses the x-axis. They occur when the output (y-value) is zero.

Front

What is the significance of the factor (x - 3) in a polynomial?

Back

The factor (x - 3) indicates that x = 3 is a root of the polynomial, meaning the polynomial equals zero when x is 3.

Front

How do you determine restrictions in rational functions?

Back

Restrictions in rational functions occur where the denominator equals zero. These values are excluded from the domain.

Front

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

Back

The roots of a polynomial are the values of x that make the polynomial equal to zero, and each root corresponds to a linear factor of the polynomial.

Front

What is the process to convert a quadratic equation to vertex form?

Back

To convert to vertex form, complete the square on the quadratic equation. This involves rearranging the equation to isolate the perfect square trinomial.

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 its linear factors and irreducible polynomials.