Question

Which of the following best describes how you can determine the x-intercepts of a polynomial function without graphing?(1 point)

Answer 1

To determine the x-intercepts of a polynomial function without graphing, you can follow these steps:

1. **Set the polynomial equal to zero**: Write the polynomial function in the form \( f(x) = 0 \).

2. **Factor the polynomial**: If possible, factor the polynomial into simpler expressions. This can help to simplify the equation.

3. **Use the Zero Product Property**: Once factored, you can set each factor equal to zero. This is based on the principle that if a product of factors equals zero, at least one of the factors must be zero.

4. **Solve for x**: Solve each equation resulting from step 3 for x. The solutions will be the x-intercepts of the polynomial function.

5. **Check for any non-real solutions**: If the polynomial is of degree higher than 2, be mindful that some solutions could be complex (non-real) numbers, which would not intersect the x-axis.

By following these steps, you can determine the x-intercepts algebraically without needing to graph the function.