Final answer:
Using algebra tiles to represent the quadratic polynomial 2x^2 + x – 6 helps visualize the factoring process. Although zero pairs are not required in this context, the equivalent factored form is determined to be (2x+3)(x–2), as the tiles can be arranged into a rectangle with these dimensions.
Step-by-step explanation:
When using algebra tiles to represent the quadratic polynomial 2x2 + x – 6, we are looking to model this expression and factor it. Algebra tiles help visualize factoring as a means of creating a rectangle where the length and width represent the factors of the expression.
To create a zero pair, we would need to add tiles that cancel out the x and unit tiles until we can arrange them in the shape of a rectangle. However, the number of zero pairs is not necessary for factoring the quadratic polynomial given, as we are simply representing the expression rather than solving an equation for x.
The equivalent factored form is identified by rearranging the tiles to create a rectangle and reading of the dimensions. For this polynomial, we start with two x2 tiles, x tiles, and -6 unit tiles. By trying different configurations to form a rectangle, we can find that the equivalent factored form is (2x+3)(x–2). This suggests that when this product is expanded, it will result in the original quadratic polynomial.