Factor Completely....?

=2x^2(12x^2+5x-2)

= 24x⁴ + 10x³ - 4x²
= 2x²(12x² + 5x - 2)

x² + 5/24x = 1/6 + (5/24)²
x² + 5/24x = 96/576 + 25/576
(x + 5/24)² = 121/576
x + 5/24 = +/- 11/24

= x + 5/24 - 11/24, = x - 6/24, = x - 1/4, = 4x - 1
= x + 5/24 + 11/24, = x + 16/24, = x + 2/3, = 3x + 2

Answer: 2x²(4x - 1)(3x + 2) are the factors.

Proof:
= 2x²(4x - 1)(3x + 2)
= 2x²(12x² + 8x - 3x - 2)
= 2x²(12x² + 5x - 2)
= 24x⁴ + 10x³ - 4x²

2x^2(4x-1)(3x+2)

24x^4 + 10x^3 - 4x^2
= 2(12x^4 + 5x^3 - 2x^2)
= 2x^2(12x^2 + 5x - 2)
= 2x^2(12x^2 + 8x - 3x - 2)
= 2x^2[(12x^2 + 8x) - (3x + 2)]
= 2x^2[4x(3x + 2) - 1(3x + 2)]
= 2x^2(3x + 2)(4x - 1)

2 x ² ( 12 x ² + 5 x - 2 )

2 x ² ( 4 x - 1 ) ( 3 x + 2 )

= 2x^2(12x^2 + 5x - 2)
= 2x^2(12x^2 + 8x -3x -2)
= 2x^2 [4x (3x + 2) -1(3x +2)]
= 2x^2 (3x + 2) (4x -1)

2x^2(12x^2+5x-2)
2x^2(12x^2-3x+8x-2)
2x^2[3x(4x-1)+2(4x-1)]
2x^2(3x+2)(4x-1)