Answer:
(x2+3) • (x2+9)
Step-by-step explanation:
Factoring [tex]x^{4} +12x^{2} +27=0[/tex]
The first term is, [tex]x^{4}[/tex] its coefficient is 1 .
The middle term is, [tex]12x^{2}[/tex] 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)
