Answer
$x(1+3x)(1-3x+9x^2)$
Work Step by Step
The formula for factoring the sum of two cubes is: $A^3+B^3=(A+B)(A^2-AB+B^2)$.
The formula for factoring the difference of two cubes is: $A^3-B^3=(A-B)(A^2+AB+B^2)$.
Hence here: $x+27x^4=\\=x(1+27x^3)\\=x(1^3+(3x)^3)\\=x(1+3x)(1^2-3x+(3x)^2)\\=x(1+3x)(1-3x+9x^2)$