SOLUTION: 3a^5-24a^2

Question 209906This question is from textbook
: 3a^5-24a^2 This question is from textbook

Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
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)

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