Question

Fill in the missing number to complete the factorization

x3 + x2 - 21x - 45 = (x + 3)(x - 5)(x +

Answer 1

3

Explanation:

Let the missing number be
`k`.

Then we have
`x^3+x^2-21x-45=(x+3)(x-5)(x+k)`

We expand the right hand side to get:

`x^3+x^2-21x-45=x^3+kx^2-2x^2-2kx-15x-15k`

By comparing constant terms we get:

`-15k=-45`

Divide both sides by -15

`k=(-45)/(-15)=3`

Therefore the missing number is 3