Find the zeros of the quadratic function by factoring. What are the \( x \)-intercepts of the graph of the function? Select the correct choice below and fill in the answer box to complete your choice. (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) A. The zeros and the x-intercepts are the same. They are B. The zeros and the x-intercepts are different. The zeros are \( \square \), the x-intercepts are

To find the zeros of a quadratic function by factoring, you first need to express the quadratic in its factored form, which looks like \( (x - p)(x - q) = 0 \). The values \( p \) and \( q \) represent the zeros of the function. You then set each factor to zero and solve for \( x \). The solutions will give you the zeros of the function, and these values also correspond to the \( x \)-intercepts of the graph since they are where the graph intersects the \( x \)-axis. So, for option A, if the factoring leads to the same \( x \)-values directly, you would say that the zeros and \( x \)-intercepts are the same. On the other hand, if the zeros differ conceptually from \( x \)-intercepts (which is often not the case), then option B would come into play. If we had an example quadratic, like \( x^2 - 5x + 6 \), we could factor it to \( (x - 2)(x - 3) \). Thus, the correct answer under A would be: "The zeros and the x-intercepts are the same. They are 2, 3."