Question

Factorise (x²-3x)²-8(x²-3x)-20.​

Answer 1

p(x) = (x²-3x)²-8(x²-3x)-20

Leta=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)