How do you factor the expression x^3 + 4x^2 + 7x + 28 by grouping?

Factoring the Expression by Grouping

To factor the polynomial expression x³ + 4x² + 7x + 28 by grouping, we can follow these steps:

Step 1: Group the Terms

We start by dividing the polynomial into two groups:

(x³ + 4x²) + (7x + 28)

Step 2: Factor Out the Common Factors

Next, we factor out the common factors from each group:

• From the first group (x³ + 4x²), we can factor out x², leading to:

x²(x + 4)

• From the second group (7x + 28), we can factor out 7, giving us:

7(x + 4)

Step 3: Combine the Factors

Now we can rewrite the expression as:

x²(x + 4) + 7(x + 4)

Notice that both terms contain the common factor (x + 4). We can factor that out:

(x + 4)(x² + 7)

Final Result

Therefore, the resulting expression after factoring x³ + 4x² + 7x + 28 by grouping is:

(x + 4)(x² + 7)