Factorize

(x square - 4x) (x square - 4x -1).- 20

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Solution

(x2 – 4x) (x2 – 4x – 1) –20

Put x2 – 4x = t

⇒ (x2 – 4x) (x2 – 4x – 1) –20 = t (t – 1) – 20 = t2 – t – 20 = t2 – 5t + 4t – 20

= t (t – 5) + 4 (t – 5) = (t + 4) (t – 5)

Put t= x2 – 4x

= (x2 – 4x + 4) (x2 – 4x – 5)

= (x2 – 2x – 2x + 4) (x2 – 5x + x – 5)

= [x ( x – 2) – 2 (x – 2)] [x ( x – 5) + 1 (x – 5)]

= (x – 2) (x – 2) (x + 1) (x – 5)

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