MathematicsFactorization 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:
     -b±b2-4ac 2a With  a = 1, b = 4 and c = −12,  we get the value of the roots as:
    -4±42-4×1×-12 2×1  -4±16+48 2   -4±64 2
      -4+82, -4-82 42, -122 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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