Which shows one way to determine the factors of x³ - 12x² - 2x + 24 by grouping?
x(x² - 12) + 2(x² - 12)
x(x² - 12) - 2(x² - 12)
x²(x - 12) + 2(x - 12)
x²(x - 12) - 2(x - 12)

Solution:

The method of grouping for factoring polynomials is a further step to the method of finding common factors. Here we aim at finding groups from the common factors, to obtain the factors of the given polynomial expression.

It is given that

x³ - 12x² - 2x + 24

Taking out x² as common in the first two terms and 2 as common in the last two terms

= x² (x - 12) - 2 (x - 12)

Therefore, the factors of x³ - 12x² - 2x + 24 by grouping are x² (x - 12) - 2 (x - 12).

Which shows one way to determine the factors of x³ - 12x² - 2x + 24 by grouping?
x(x² - 12) + 2(x² - 12)
x(x² - 12) - 2(x² - 12)
x²(x - 12) + 2(x - 12)
x²(x - 12) - 2(x - 12)

Summary:

x² (x - 12) - 2 (x - 12) shows one way to determine the factors of x³ - 12x² - 2x + 24 by grouping.