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)

x²(x - 12) - 2(x - 12) shows one way to determine the factors  x³ - 12x² - 2x + 24 by grouping ⇒ 4th answer

Step-by-step explanation:

In grouping factorization we factorize each two terms to find a common bract between the terms after the factorization

Ex: ax² + by - bx² - ay, lets take the terms ax² , -ay in a bracket and -bx² , by in other bracket

ax² + by - bx² - ay = (ax² - ay) + (-bx² + by)

Take a as a common factor from (ax² - ay) and -b as a common factor from (-bx² + by)

(ax² - ay) + (-bx² + by) = a(x² - y) + -b(x² - y), remember (+)(-) = (-),

then (ax² - ay) + (-bx² + by) = a(x² - y) - b(x² - y)

Now let us solve the problem

∵ The expression is x³ - 12x² - 2x + 24

- Let us take x³ , -12x² in a bracket and -2x , 24 in other bracket

∴  x³ - 12x² - 2x + 24 = (x³ - 12x²) + (-2x + 24)

∵ The common factor of x³ and -12x² is x²

- Divide each term in the bract by x² to find the rest terms in the

   bracket

∵ x³ ÷ x² = x

∵ -12x² ÷ x² = -12

∴ (x³ - 12x²) = x²(x - 12)

∵ The common factor of -2x and 24 is -2

- Divide each term in the bract by -2 to find the rest terms in the

   bracket

∵ -2x ÷ -2 = x

∵ 24 ÷ -2 = -12

∴ (-2x + 24) = -2(x - 12)

∴ (x³ - 12x²) + (-2x + 24) = x²(x - 12) + -2(x - 12)

∵ (=)(-) = (-)

∴ (x³ - 12x²) + (-2x + 24) = x²(x - 12) - 2(x - 12)

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

there is no question content here, but you for the free points! : d