Sure, let's take a close look and rewrite the given expression in its complete factored form.
The expression is:
[tex]\[ q^2(u-9) + c(u-9) \][/tex]
Step 1: Identify the common factor in both terms.
Notice that [tex]\((u-9)\)[/tex] is a common factor in both terms.
Step 2: Factor out the common term [tex]\((u-9)\)[/tex].
When we factor out [tex]\((u-9)\)[/tex], we are left with [tex]\(q^2\)[/tex] from the first term and [tex]\(c\)[/tex] from the second term.
Thus, the expression can be factored as:
[tex]\[ (u-9)(q^2 + c) \][/tex]
So the complete factored form is:
[tex]\[ (u-9)(q^2 + c) \][/tex]
Therefore, the final answer is:
[tex]\[ (u-9)(q^2 + c) \][/tex]
