Question

Factorize the following polynomial:- 1. (x²-x)²-8(x²-x)+12​

Answer 1

Solution :-

The polynomial is:-

$( {x}^{2} - x) {}^{2} - 8(x {}^{2} - x) + 12 \\ y = (x {}^{2} - x)$

Then the polynomial becomes,

$y {}^{2} - 8y + 12$

$y {}^{2} - 6y - 2y + 12$

$y(y - 6) - 2(y - 6)$

$(y - 2)(y - 6)$

$( {x}^{2} - x - 2)( {x}^{2} - x - 6)$

Now normal factor van be further factorise ,

$( {x}^{2} - 2x + x - 2)( {x}^{2} - 3x + 2x - 6)$

${x(x - 2) + 1(x - 2)} \: {x(x - 3) + 2(x - 3)}$

$(x + 1)(x - 2)(x + 2)(x - 3).$

Hence Proved