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)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)