Factorization of (x2+x)2+4(x2+x)−12 will be ____.

# Factorization of (x2+x)2+4(x2+x)−12 will be ____.

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### Solution:

To solve the question, we first equate the value of  x terms from the quadratic equation (x2+x)2 + 4(x2+x) − 12   where we take the value of  x2 + x  as t. Using the value of  t, we form a new quadratic equation where we find the equation as:
⇒ (x
2+x)2 + 4(x2+x) − 12
⇒ (t)2 + 4(t) − 12
Now let us find the roots of the above equation, by using the quadratic formula:
With  a = 1, b = 4 and c = −12,  we get the value of the roots as:

Hence, the value of the roots of the quadratic equation in terms of t  is given as:
⇒ 2, −6

Now we equate the value of the t in terms of x2+x, we get the value of x as:
For 2: c = 2 or x2+x = 2  and
For −6: c = −6 or x2+x = −6
Taking the two roots we are equating to the value of c with x2+x  and the two roots we get are:    x2+x = 2, x2+x = −6 or (x2+x−2), (x2+x+6)
Therefore, the factorization of (x2+x) 2+4(x2+x)−12 is (x2+x−2), (x2+x+6) .
So, the correct answer is “(x2+x−2), (x2+x+6)”.

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