Question

Factorise: (x^2 - 3x)^2 - 8(x^2 - 3x) - 20

Answer 1

Answer:

Solution:

p(x) = (x²-3x)²-8(x²-3x)-20

Let a = x²-3x

Now ,

p(x) = a²-8a-20

splitting the middle term,we get

=> p(x) = a²-10a+2a-20

= a(a-10)+2(a-10)

= (a-10)(a+2)

= (x²-3x-10)(x²-3x+2)

= (x²-5x+2x-10)(x²-2x-1x+2)

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

= (x-5)(x+2)(x-2)(x-1)

Therefore,

p(x)=(x-5)(x+2)(x-2)(x-1)

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