Question

(x²-x)²-8(x²-x)+12, Factorize the given polynomial.

Answer 1

Let x^2 - x = a

= a^2 - 8a + 12

= a^2 - 6a - 2a + 12

= a(a-6) - 2(a-6)

= (a-6)(a-2)

= ( x^2 - x - 6)(x^2 - x - 2)

= [ x^2 - 3x + 2x - 6] [x^2 - 2x + x - 2]

= [ x(x-3) + 2(x-3)] [x(x-2) + 1(x-2)]

= (x-3)(x+2)(x+1)(x-2)

Answer 2

Given (x²-x)-8(x²-x)+12

Splitting the middle term,

= (x²-x)²-6(x²-x)-2(x²-x)+12

=(x²-x)[x²-x-6]-2[x²-x-6]

=(x²-x-6)(x²-x-2)

= [x²-3x+2x-6][x²-2x+x-2]

=[x(x-3)+2(x-3)][x(x-2)+1(x-2)]

=[(x-3)(x+2)][(x-2)(x+1)]

=(x-2)(x-3)(x+1)(x+2)

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