Factories the following

2x – 32x⁵

In given expression

Take out the common factor,

[2 × x - 2 × 2 × 2 × 2 × 2 × x × x × x × x × x]

⇒ 2 × x[1 - 2 × 2 × 2 × 2 × x × x × x × x]

⇒ 2x [1-16x⁴] = 2x [1-(2x)⁴]

⇒ In the term 1-(2x)⁴

= 1-(4x²)²

Both terms are perfect square

⇒ (4x² )² = 4x² × 4x²

⇒ 1 = 1 × 1

∴ 1-(4x²)² Seems to be in identity a²-b² = (a + b)(a-b)

Where a = 1 and b = 4x²;

1-16x⁴ = (1-4x²)(1 + 4x²)

→ 1-4x² = 1-(2x)²

∴ 1-4x² Seems to be in identity a²-b² = (a + b)(a-b)

Where a = 1 and b = 2x;

1-4x² = (1-2x)(1 + 2x)

∴ 1-16x² = (1-2x)(1 + 2x) (1 + 4x²)

Hence the factors of 2x – 32x⁵ are 2x,(1-2x),(1 + 2x) and (1 + 4x²)