We are given the equation:
x (y + 6) – 5 (y + 6) ---> 1
We are to look for the missing factor in the equation: (_) (y + 6) from the given values.
Knowing the rules of the polynomial multiplicity, we can have an idea that the given equation can also be written in the form of:
(x – 5) (y + 6) ---> 2
wherein the whole factor (y + 6) was simply distributed to the values in the factor (x – 5). To prove that equations 1 and 2 are equal:
x (y + 6) – 5 (y + 6) = (x – 5) (y + 6)
Expanding:
x y + 6 x - 5 y – 30 = x y + 6 x – 5 y – 30 (EQUAL!)
Therefore our missing factor is:
(x – 5)