Question

Find Quotient and the remainder

X^3+216a^3 divides by x+6a

Answer 1

You could do a long algebraic division, make sure you have

(x^3 + 0x^2 + 0x + 216a^3) ÷ (x + 6a)

or
you could recognize the sum of cubes factoring
x^3 + 216a^3
= x^3 + (6a)^3
= (x+6a)(x^2 - 6ax + 36a^2) , with 0 remainder

expand it to see that I am right

Answer 2

********** x^2 - 6 a x + 36 a^2
*********--------------------------------------
x + 6 a | x^3 + 0 x^2 + 0 x + 216 a^3
********* x^3 + 6 a x^2
********------------------
****************-6 a x^2 + 0 x + 216 a^3
****************-6 a x^2 -36 a^2 x
**************-----------------------------------
*************************36 a^2 x + 216 a^3
*************************36 a^2 x + 216 a^3
************************* -----------------------
*********************************** 0