Factor by grouping. \[ x^{3}-9 x^{2}+5 x-45 \] Select the correct choice below and fill in any answer boxes within your choice. B. The polynomial is prime. Bx \( 25 x-45= \)

Let's dive into factoring by grouping! First, we’ll rearrange and group terms: \[ (x^3 - 9x^2) + (5x - 45) \] Now, we factor out common elements from each group: \[ x^2(x - 9) + 5(x - 9) \] Next, notice that both groups contain a common factor of \( (x - 9) \): \[ (x - 9)(x^2 + 5) \] Given \( x^2 + 5 \) doesn't factor nicely over the reals (since it has no real solutions), our fully factored form is: \[ (x - 9)(x^2 + 5) \] Now you're ready to tackle any challenge fueled by this newfound knowledge!