Alg 2 - Zeros vs. Factors

Front

What is a zero of a polynomial function?

Back

A zero of a polynomial function is a value of x for which the function evaluates to zero. It is also known as a root of the polynomial.

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. If (x - r) is a factor, then r is a zero of the polynomial.

Front

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

Back

To find the zeros of a polynomial, set each factor equal to zero and solve for x.

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, while the factors are the expressions that can be multiplied to obtain the polynomial.

Front

What is the corresponding solution of the factor (4x + 3)?

Back

x = -3/4.

Front

What is the corresponding factor of the solution x = 2?

Back

(x - 2).

Front

What is the corresponding factor of the solution x = -5/4?

Back

(4x + 5).

Front

What is the corresponding solution of the factor (x + 8)?

Back

x = -8.

Front

How can you determine if a number is a zero of a polynomial?

Back

Substitute the number into the polynomial. If the result is zero, then it is a zero of the polynomial.

Front

What is the significance of finding zeros in polynomial functions?

Back

Finding zeros helps in graphing the polynomial function, as they indicate the x-intercepts of the graph.