Question

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

x⁴ + 5x² + 9

Answer 1

Given expression: x⁴ + 5x² + 9

Now, using middle term factorisation method,

x⁴ + 5x² + 9

= x⁴ + 6x² – x² + 9

= x⁴ + 6x² + 9 – x²

= (x² + 3)² – x²  ...[∵ (a + b)² = a² + 2ab + b²]

= (x² + 3 + x) (x² + 3 – x)  ...[∵ a² – b² = (a + b) (a – b)]

The factorisation result is (x² + 3 + x) (x² + 3 – x).