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Let us assume that x-y=c
Therefore, c2−4c−45=0;
or, c2−9c+5c−45=0;
or, (c+5)(c−9)=0;
i.e, c=-5 or c=9;
So, either, x-y=-5 or x-y+5 is a factor.
Or, x-y=9 or x-y-9 is a factor.
Hence, c is the correct option.
Hope, it helped.
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Given Equation is (x - y)^2 - 4(x - y) - 45
Let (x - y) = a.
⇒ a^2 - 4a - 45
⇒ a^2 - 9a + 5a - 45
⇒ a(a - 9) + 5(a - 9)
⇒ (a - 9)(a + 5),
Then,
⇒ (x - y - 9)(x - y + 5).
So, one of the factor is (x - y - 9) - Option (C).
Hope this helps!