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No, they cannot with real numbers. With complex numbers it is possible.
It means that the question has been written by someone who does not know what the word "polynomial" means, or else that this is a copy-and-paste by someone who knows even less! Only a trinomial can be written as a product of two binomials. No polynomial of any other order can!
The two binomials can be written as (x - a)(x + a), for any constant a. Proof: Expand using FOIL: (x - a)(x + a) = x2 + xa - xa - a2 Group: (x - a)(x + a) = x2 - a2 x2 - a2 is a difference of squares. Thus, the product of (x - a) and (x + a) is a difference of squares.
No. A counter-example proves the falsity: Consider the two binomials (x + 2) and (x - 2). Then (x + 2)(x - 2) = x2 - 2x + 2x - 4 = x2 - 4 another binomial.
Carolus Linnaeus