Question

Which statement is true about the prime polynomial 2x2 + 3x + 3?

It cannot be modeled with a rectangle.
It can be modeled with a square.
It cannot be modeled with all positive tiles.
It can only be modeled with an odd number of tiles.

Answer 1

"It cannot be modeled with a rectangle."

Reason: 2x^2+3x+3 is irreducible over the integers (discriminant 9−24=−15), so it does not factor as the product of two integer-coefficient binomials and therefore cannot be arranged as a rectangular area model (product of two integer-side binomials). It is not a perfect square, it does consist of 8 positive tiles (so it can be represented as positive tiles), and it does not require an odd number of tiles.