Question

Factorise: x⁴ - 5x² - 36

Answer 1

x⁴ - 5x² - 36

= (x²)² - 5x² - 36

= (x²)² - 9x² + 4x² - 36    ...{∵ -36 = -9 × 4 }
                                            {-5 = -9 + 4}

= x² (x² - 9) +  (x² - 9)

= (x² - 9)(x² + 4)

= [x² - (3)²] [x² + 4]

= (x + 3)(x - 3)(x² + 4)

= (x² +4) (x + 3)(x - 3)