Factor the following polynomial completely. $3 a ^ { 4 } - 243$
A) $3 ( a + 3 ) \left( a ^ { 2 } + 9 \right)$
B) $3 \left( a ^ { 2 } - 9 \right) \left( a ^ { 2 } + 9 \right)$
C) $3 ( a - 3 ) ( a + 3 ) \left( a ^ { 2 } + 9 \right)$
D) $( a - 3 ) ( a + 3 ) \left( a ^ { 2 } + 9 \right)$
E) none of these

Question

Quizplus · Accepted Answer

First, we can rearrange the polynomial to be in the form of a difference of two perfect squares: 
$$3a^4 - 243 = 3(a^4 - 81)$$ 
Then, we can use the formula for the difference of two perfect squares: 
$$a^4 - 81 = (a^2)^2 - 9^2 = (a^2 -9)(a^2 + 9)$$ 
Substituting this back in, 
$$3(a^4 - 81) = 3(a^2-9)(a^2+9) = 3(a-3)(a+3)(a^2+9)$$ 
Therefore, the correct choice is C.

Factor the Following Polynomial Completely 3a4−2433 a ^ { 4 } - 2433a4−243

Factor the Following Polynomial Completely $3 a ^ { 4 } - 243$