Question

Factor X^4+12x^2+27=0

Answer 1

Answer:

(x2+3)  •  (x2+9)

Step-by-step explanation:

Factoring $x^{4} +12x^{2} +27=0$

The first term is,  $x^{4}$  its coefficient is  1 .

The middle term is,  $12x^{2}$  its coefficient is  12 .

The last term, "the constant", is  +27  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 27 = 27  

Step-2 : Find two factors of  27  whose sum equals the coefficient of the middle term, which is   12 .

     27    +    1    =    28  

     9    +    3    =    12    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -3  

                    x4 + 9x2 + 3x2 + 27

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x2 • (x2+9)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x2+9)

Step-5 : Add up the four terms of step 4 :

                   (x2+3)  •  (x2+9)