Question

Fill in the missing number to complete the factorization
x3 + x2 - 21x - 45 = (x + 3)(x - 5)(x +

Answer 1

Answer:

3

Step-by-step 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

$k=\frac{-45}{-15}=3$

Therefore the missing number is 3