Question

factorize...plz ans fast​

Answer 1

Question:-

Factorise :-

(x² + x)² - 8(x² + x) + 12

Answer:-

(x² + x)² - 8(x² + x) + 12

Let x² + x be a

= a² - 8a + 12

Now performing middle term splitting,

= a² - 6a - 2a + 12

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

= (a - 6)(a - 2)

Now substituting value of a in terms of x,

= (x² + x - 6)(x² + x - 2) ----------(i)

Now let's look at the first and second term individually,

1st term ==> (x² + x - 6)

We can further factorise it by middle term splitting,

x² + x - 6

= x² + 3x - 2x - 6

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

= (x + 3)(x - 2)

2nd term ==> (x² + x - 2)

We can further factorise it by middle term splitting,

x² + x - 2

= x² + 2x - x - 2

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

= (x + 2)(x - 1)

Now putting the factorised value of 1st term and 2nd in equation (i) :-

(x² + x - 6)(x² + x - 2)

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