how to factor x power3+7?

Answer 1

x^3 +7 has 3 factors, One is real and two are complex.
x = -cuberoot(-7), so one factor is (x+cuberoot(-7)).
Now use long division to find (x^3 +7)/(x+cuberoot(-7)).
Use the quadratic formula on the quotient to find the other two complex factors.

Answer 2

You have an irreducible polynomial there, one which will not factor. If your course asked you to factor it i hope they gave you the tools to prove it's prime. If not let's do it . The smallest factors of x^3 + 7 would have to be selected from,


(x + 1), (x + 7), (x - 1), or (x - 7)


but these leave remainders of


6 , -336, 8, and 350


when divided into x^3 + 7.

This means that x^3 + 7 does not have polynomial factors with integer coefficients. What about non integer coefficients?

x^3 + 7 = x^3 + (7^(1/3) )^3 (the sum of two cubes)

=( x + 7^(1/3))(x^2 - x 7^(1/3) + 7^(2/3)).

and you may break down the larger term .