The polynomial remainder theorem says when we divide polynomial f(x) by x-a we'll get remainder f(a).
[tex]f(x)=x^3 - 3x^2 - 31x - 72[/tex]
[tex]f(8)=8^3 - 3(8^2) - 31(8) - 72[/tex]
[tex]f(8)=512 - 3(64) - 31(8) - 72 = 512-192-248-72 = 0[/tex]
Since f(8)=0 that means x-8 has a remainder zero when divided by f(x). In other words, it's a factor of f(x).
Answer B
