Can a square have an area of 4x^2-4x-1?

Answer 1

A square is defined as shape having four equal side lengths (L).

That means the area of a square is A=L²

That means you need to see if your polynomial is a perfect square (or is it is factorable into two equal terms, which have equal solutions)

4x²-4x-1 Can be factored, but not into equal terms

(2x-2.4)(2x+0.4) not equal

Not the area of a square

If the function was instead

4x²-4x+1 can be factored into equal terms and would be a the area of a square

(2x-1)² equal lengths, yes a square

Answer 2

Answer 3

No, as the last term in that polynomial is negative, there is no way to factor that into a perfect square binomial.