Question

HØLÅ

FACTORISE THE POLYNOMIALS

( x ² - x ) ² - 8 ( x ² - x ) + 12

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Answer 1

Let (x² - x) be y.

So,

${y}^{2} - 8y + 12 \\ = {y}^{2} - 6y - 2y + 12 \\ = y(y - 6) - 2(y - 6)\\ = (y - 6)(y - 2) \\ = ( {x}^{2} - x - 6)( {x}^{2} - x - 2) \\ = ( {x}^{2} - 3x + 2x - 6)( {x}^{2} - 2x + x - 2) \\ = (x(x - 3) + 2(x - 3))(x(x - 2) + 1(x - 2)) \\ = (x - 3)(x + 2)(x - 2)(x + 1).$

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