Question

Factorise:x⁴+5x²+9 Thank you

Answer 1

Given, x⁴ + 5x² + 9 to factorise
           = x⁴ + 6x² + 9 - x²
           = [(x²)² + 2×3×(x²) + 3²] - (x)²
           = (x² + 3)² - x²
It is in the form of a²-b² which can be written as (a+b)(a-b)
           = (x²+3-x)(x²+3+x)

∴ x⁴+5x²+9 = (x²+3-x)(x²+3+x)

Answer 2

[x^4 + 5x²+9]
adding and subtracting x²,
=[x^4 +5x² +x² +9] -x²
=(x^4 +6x² +9) - x²
=(x²+3)² - x²
=(x²+3 +x)(x²+3 -x)