Factorize the polynomials. (x2 – 6x)2 – 8(x2 – 6x + 8) – 64

1.	Factorize the polynomials. (x2 – 6x)2 – 8(x2 – 6x + 8) – 64
Answer» (x² – 6x)² – 8(x² – 6x + 8) – 64 = m² – 8(m + 8)-64 …[Putting x² – 6x = m] = m² – 8m – 64 – 64 = m² – 8m – 128 = m² – 16m + 8m- 128 = m(m – 16) + 8(m – 16) = (m – 16)(m + 8) = (x² – 6x – 16) (x² – 6x + 8) … [Replacing m = x² – 6x] = (x² – 8x + 2x – 16) (x² – 4x – 2x + 8) = [x(x – 8) + 2(x – 8)] [x(x – 4) – 2(x – 4)] = (x – 8) (x + 2) (x – 4) (x – 2)

Answer»

(x² – 6x)² – 8(x² – 6x + 8) – 64

= m² – 8(m + 8)-64 …[Putting x² – 6x = m]

= m² – 8m – 64 – 64

= m² – 8m – 128

= m² – 16m + 8m- 128

= m(m – 16) + 8(m – 16)

= (m – 16)(m + 8)

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

= (x² – 8x + 2x – 16) (x² – 4x – 2x + 8)

= [x(x – 8) + 2(x – 8)] [x(x – 4) – 2(x – 4)]

= (x – 8) (x + 2) (x – 4) (x – 2)

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