Question

If x+3 is one factor of x^3 +27 what is the other factor

Answer 1

Work is provided in the image attached.

Answer 2

For this case we have the following third degree polynomial:
 $x ^ 3 +27$
 By completely factoring the polynomial we have:
 $(x + 3) (x ^ 2 - 3x + 9)$
 We will verify that the factorization is correct.
 For this, we make distributive property:
 $(x ^ 3 - 3x ^ 2 + 9x) + (3x ^ 2 - 9x + 27)$
 We add similar terms:
 $x ^ 3 + (-3x ^ 2 + 3x ^ 2) + (9x - 9x) + 27 x ^ 3 +27$
 Therefore, the factorization is correct.
 So, the other factor is:
 $(x ^ 2 - 3x + 9)$
 Answer:
 the other factor is:
 $(x ^ 2 - 3x + 9)$