Answer
$3x^2(x+2)(x^2-4x+4)$
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: $3x^5+24x^2=\\=3x^2(x^3+8)\\=3x^2(x^3+2^3)\\=3x^2(x+2)(x^2-4x+4)$
