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Question

Factorise: (x2−5x)(x2−5x−20)+84

A
(x6)(x+1)(x7)(x+2)
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B
(x6)(x1)(x7)(x+2)
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C
(x6)(x+1)(x7)(x2)
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D
(x6)(x3)(x7)(x+2)
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Solution

The correct option is A (x6)(x+1)(x7)(x+2)
(x25x)(x25x20)+84=(x25x)(x25x)20(x25x)+84
=(x25x)220(x25x)+84
Let x25x=a. Then, the given expression
=a220a+84=a216a14a+84
=a(a6)14(a6)=(a6)(a14)
=(x25x6)(x25x14)=(x26xx+6)(x27x+2x16)
=[x(x6)+1(x6)][x(x7)+2(x7)]
=(x6)(x+1)(x7)(x+2)

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