|
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)
|
|
|
| |
