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The polynomial $a − b − a 2 + b 2$ has [[1]] factors.

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answer is TWO.

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Detailed Solution

The polynomial

a − b − a 2 + b 2

has two factors.
The given polynomial is

a − b − a 2 + b 2 .

The given polynomial can be written as

a − b − (a 2 − b 2) .

We know that

a 2 − b 2 = (a − b) (a + b) .

Thus we have,

a − b − a 2 + b 2 = a − b − (a 2 − b 2) ⇒ a − b − a 2 + b 2 = a − b − {(a − b) (a + b)}

Taking out the common terms from the reduced polynomial, we get,

a − b 1 − {a + b} = a − b 1 − a − b

Therefore, the factors of the polynomial

a − b − a 2 + b 2

are

a − b

and

(1 − a − b) .

Thus, the polynomial

a − b − a 2 + b 2

has two factors.

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