Question
Which of the following best describes how you can determine the x-intercepts of a polynomial function without graphing?(1 point)
Responses
Find the value of the function when x equals zero.
Find the value of the function when x equals zero.
Find the number of terms of the polynomial function.
Find the number of terms of the polynomial function.
Find the degree of the polynomial function.
Find the degree of the polynomial function.
Find the zeros of the polynomial function.
Find the zeros of the polynomial function.
The correct response is:
Find the zeros of the polynomial function.
To determine the x-intercepts of a polynomial function without graphing, you need to find the zeros of the function. These are the values of x for which the function equals zero. This can be done by setting the polynomial equal to zero and solving for the values of x.
To determine the x-intercepts of a polynomial function without graphing, you can follow these steps:
Step 1: Find the zeros of the polynomial function
The x-intercepts of a polynomial function are the values of x for which the function equals zero. To find these values, set the polynomial function equal to zero and solve for x. This can be done by factoring the polynomial, using the quadratic formula, or using other methods such as synthetic division or long division.
Step 2: Verify the answers
After finding the zeros of the polynomial function, substitute each value back into the original polynomial function and check if the function value is indeed zero. This step is important to ensure that the values you found are true x-intercepts.
Therefore, the correct response is "Find the zeros of the polynomial function."