Question

Factorize the polynomials.

(x² – x)² – 8(x² – x) + 12

Answer 1

(x² – x)² – 8(x² – x) + 12

= m² – 8m + 12 …[Putting x² – x = m] 

= m² – 6m – 2m + 12 

= m(m – 6) – 2(m – 6) 

= (m – 6)(m – 2) 

= (x² – x- 6) (x² – x- 2) …[Replacing m = x² -x]

= (x² – 3x + 2x – 6) (x² – 2x + x – 2) 

= [x(x – 3) + 2(x – 3)] [x(x – 2) + 1 (x-2)] 

= (x – 3) (x + 2) (x – 2) (x + 1)