Factorize the polynomials. (x – 3) (x – 4)2 (x – 5) – 6

1.	Factorize the polynomials. (x – 3) (x – 4)2 (x – 5) – 6
Answer» (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]

Answer»

(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]

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