Question

Factorise by splitting the middle term to get two perfect squares. 

x⁴ + 3x² + 4

Answer 1

Given expression: x⁴ + 3x² + 4

Now, using middle term factorisation method,

x⁴ + 3x² + 4

= x⁴ + 4x² – x² + 4

= x⁴ + 4x² + 4 – x²

= (x² + 2)² – x²   ...[∵ (a + b)² = a² + 2ab + b²]

= (x² + 2 + x) (x² + 2 – x)   ...[∵ a² – b² = (a + b)(a – b)]

The factorisation result is (x² + 2 + x) (x² + 2 – x).