If you mean x^3 + 7^2 + 15x + 9 then:
x^3 + 49 + 15x + 9
x^3 + 15x + 58 does not have any rational zeros. (can't factor)
If you mean x^3 + x^2 + 15x + 9 then:
. . .it also appears to not have any rational zeros.
If you mean x^3 + 7x^2 + 15x + 9 then:
Let's try -1. . .
f(x) = x^3 + 7x^2 + 15x + 9
f(-1) = -1 + 7 - 15 + 9
f(-1) = 0
So -1 should work as a root, meaning we should be able to factor out (x+1).
Note: If -1 is a root then x = -1 means x + 1 = 0, which means (x+1) should be a factor in x^3 + 7x^2 + 15x + 9
(x + 1)(???x^2 + ??x + ?) = x^3 + 7x^2 + 15x + 9
x * ???x^2 = x^3, so ??? = 1
1 * ? = 9, so ? = 9
(x + 1)(x^2 + ??x + 9) = x^3 + 7x^2 + 15x + 9
The 15x comes from x * 9 + ??x * 1:
9x + ??x = 15x
??x = 6x
?? = 6
(x + 1)(x^2 + 6x + 9) = x^3 + 7x^2 + 15x + 9
(x + 1)(x + 3)(x + 3)
Answer: (x+1)(x+3)^2