Question

Factor 16x2 + 24x + 9. (4 x + 3) 2 (16 x + 3)( x + 3) (4 x + 3)(4 x - 3)

Answer 1

(4x + 3)²

Explanation:

Given

16x² + 24x + 9

This is a perfect square of the form

(ax + b)² = a²x² + 2abx + b²

Compare coefficients to 16x² + 24x + 9, that is

a² = 16 ⇒ a =
`√(16)` = 4

b² = 9 ⇒ b =
`√(9)` = 3

and 2ab = 2 × 4 × 3 = 24

Thus

16x² + 24x + 9 = (4x + 3)²