Factor the polynomial 4x^4 + 20x^2 + 3x^2 + 15 by grouping. What is the resulting expression?

To factor the polynomial 4x⁴ + 20x² + 3x² + 15 by grouping, we start by reorganizing the expression:

(4x⁴ + 20x²) + (3x² + 15)

Now, we can factor out common factors from each group:

• From the first group 4x⁴ + 20x², we can factor out 4x²:

4x²(x² + 5)

• From the second group 3x² + 15, we can factor out 3:

3(x² + 5)

Now, we have:

4x²(x² + 5) + 3(x² + 5)

Notice that (x² + 5) is a common factor. We can factor it out:

(x² + 5)(4x² + 3)

Thus, the resulting expression after factoring by grouping is:

(x² + 5)(4x² + 3)