Question

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

Answer 1

(x2+3) • (x2+9)

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)