Answer:
3
Step-by-step explanation:
Let the missing number be [tex]k[/tex].
Then we have [tex]x^3+x^2-21x-45=(x+3)(x-5)(x+k)[/tex]
We expand the right hand side to get:
[tex]x^3+x^2-21x-45=x^3+kx^2-2x^2-2kx-15x-15k[/tex]
By comparing constant terms we get:
[tex]-15k=-45[/tex]
Divide both sides by -15
[tex]k=\frac{-45}{-15}=3[/tex]
Therefore the missing number is 3
