Question 209906
No instructions were given but I assume you want to factor.


Factor out the common factor 3a^2 and then divide each term of the polynomial by the common factor.

3a^5 divided by 3a^2 = a^3

-24a^2 divided by 3a^2 = -8

We now have:


3a^2(a^3 - 8)


However, inside the parenthese we have the difference of two perfect cubes.

We must factor what's inside the parentheses.


We use the formula to do so:


a^3 – b^3 = (a – b)(a^2 + ab + b^2) 


Now, a^3 - 8 can be rewritten as a^3 - 2^3.

NOTE: 8 = 2^3 (in case you're wondering where 2^3 came from).


We now plug that into the formula and simplify.

a^3 - 2^3 = (a - 2)(a^2 + 2a + 4)

Final answer: (3a^2)(a - 2)(a^2 + 2a + 4)