Factor x^3 + 4x^2 + 7x + 28 by Grouping – What is the Resulting Expression?

To factor the expression x³ + 4x² + 7x + 28 by grouping, we can break it into two groups.

First, we group the first two terms and the last two terms:

(x³ + 4x²) + (7x + 28)

Now, we can factor out the greatest common factor (GCF) from each group:

From the first group, x² can be factored out:

1. x²(x + 4)

From the second group, 7 can be factored out:

2. 7(x + 4)

Now we combine these factored groups:

x²(x + 4) + 7(x + 4)

Notice that (x + 4) is now a common factor:

We can factor it out:

(x + 4)(x² + 7)

Thus, the resulting expression after factoring by grouping is:

(x + 4)(x² + 7)