Which shows one way to determine the factors of x³ - 9x² + 5x - 45 by grouping
x²(x - 9) - 5(x - 9)
x²(x + 9) - 5(x + 9)
x(x² + 5) - 9(x² + 5)
x(x² - 5) - 9(x² - 5) 

Solution:

Given: Polynomial is x³ - 9x² + 5x - 45

One of the methods to factor a polynomial is by grouping. Group the polynomial in such a way that the common factors can be taken out from the first two terms and again from the last two terms. Rewriting we get,

x³ + 5x - 9x² - 45

= x(x² + 5) - 9(x² + 5)

Taking out (x² + 5) as the common factor again, we get

(x² + 5)(x² - 9)

Therefore, the factors obtained by grouping are (x² + 5)(x² - 9).

Which shows one way to determine the factors of x³ - 9x² + 5x - 45 by grouping?

Summary:

The factors of x³ - 9x² + 5x - 45 by grouping are (x² + 5)(x² - 9).