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State true or false: The factors of $a b c − a b − c + 1$ are $(c − 1)$ and $(a b − 1)$ .

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False

True

answer is A.

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Detailed Solution

The given expression is as follows,

a b c − a b − c + 1

.
It can be observed that there are no common factors in the terms of the expression.
So, let us proceed with regrouping the terms with common factors as follows,

(a b c − a b) + (− c + 1)

Now, we can factor out the terms which are common in each of the groups as follows,

a b (c − 1) − 1 (c − 1) = (c − 1) (a b − 1)

So, the factors of

a b c − a b − c + 1

are

(c − 1)

and

(a b − 1)

.
Hence, the given statement is true.
So, the correct option is 1.

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