Missing number to complete the factorization is 3.
What is factorization?
Factorization can be defined as the process of breaking down a number into smaller numbers which when multiplied together arrive at the original number. These numbers are broken down into factors or divisors.
Given expression
\(x^{3}+x^{2} -21x-45=(x+3) (x-5) (x+a)\)
Let a be the missing number
(x + 3) (x - 5) (x + a)
= \((x^{2} -5x+3x-15)(x+a)\)
= \((x^{2} -2x-15)(x+a)\)
\(x^{3}+x^{2} -21x-45=x^{3} +x^{2} a-2x^{2} -2xa-15x-15a\)
By comparing the expressions
-2xa - 15x = -21x
⇒ -2xa = -6x
⇒ a = 3
\(x^{2} (a-2) = 1x^{2}\)
⇒ a - 2 = 1
⇒ a = 3
-15a = -45
⇒ a = 3
Hence, missing number to complete the factorization is 3.
Find out more information about factorization here
https://brainly.com/question/12087111
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