Question

Factorize the polynomials. 

(x – 3) (x – 4)² (x – 5) – 6

Answer 1

(x – 3) (x – 4)² (x – 5) – 6 

= (x – 3) (x – 5) (x – 4)² – 6 

= (x² – 5x – 3x + 15) (x² – 8x + 16) – 6 

= (x² – 8x + 15) (x² – 8x + 16) – 6 

= (m + 15) (m+ 16) – 6 … [Putting x² – 8x = m]

 = m (m + 16) + 15 (m + 16) – 6 

= m² + 16m + 15m + 240 – 6 

= m² + 31m + 234 

= m² + 18m + 13m + 234

= m(m + 18) + 13(m + 18) 

= (m + 18) (m + 13)

= (x² – 8x + 18) (x² – 8x + 13) … [Replacing m = x² – 8x]