Question

1. Factorize the following polynomials.
(i) (x2 - x)2 - 8(r? - x) +12​

Answer 1

Answer

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 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)

Answer verified

Answer 2

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 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)