Question

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

1) x(x² – 12) + 2(x² – 12)
2) x²(x – 12) + 2(x – 12)
3) x(x² – 12) – 2(x² – 12)
4) x²(x – 12) – 2(x – 12)

Answer 1

Option 2) x²(x – 12) + 2(x – 12) is the correct way to determine the factors of x³ – 12x² – 2x + 24 by grouping.

Step-by-step explanation:

The correct option to determine the factors of x³ – 12x² – 2x + 24 by grouping is option 2) x²(x – 12) + 2(x – 12).

To factor the expression by grouping, we need to regroup the terms in pairs and factor them separately. In this case, we can group the first two terms and the last two terms:

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

Now, factor the common terms out of each group:

= x²(x – 12) + 2(x – 12)

Now we have a common factor of (x – 12) in both terms, so we can further factor the expression:

= (x – 12)(x² + 2)

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