Which is the completely factored form of 4x² + 28x + 49?
(x + 7)(4x + 7)
4(x + 7)(x + 7)
(2x + 7)(2x + 7)
2(x+7)(x + 7)

Solution:

Given polynomial is 4x² + 28x + 49

Factoring polynomials is done in many ways. Let us use the algebraic identity to factor this.

⇒ 4x² +28x + 7²

⇒ 4x² +2(14)(x) + 7²

⇒ (2x)² + 2(2x)(7) + 7²

This is similar to a² + 2ab + b² = (a + b)²

⇒ (2x + 7)²

⇒ (2x + 7)(2x + 7)

Which is the completely factored form of 4x² + 28x + 49?

Summary:

The completely factored form of 4x² + 28x + 49 is (2x + 7)(2x + 7).