Question

1) Factorise the given polynomial :
(x2 – x)2 – 8 (x2 – x) + 12.​

Answer 1

Answer:

The polynomial is

(x2−x)2 −8(x 2 −x)+12

y=(x2−x)

Step-by-step explanation:

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 both factors can be further factorized,

(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)