Question

The model represents a polynomial and its factors.

An algebra tile configuration. 4 tiles are in the Factor 1 spot: 1 is labeled + x and 3 are labeled negative. 2 tiles are in the Factor 2 spot: 1 is labeled + x and 1 is labeled negative. 8 tiles are in the Product spot: 1 is labeled + x squared, 4 are labeled negative x, and 3 are labeled +.
Which equation is represented by the model?

x2 – 2x – 3 = (x – 3)(x + 1)
x2 – 4x + 3 = (x – 3)(x – 1)
x2 + 2x + 3 = (x + 3)(x – 1)
x2 + 4x – 3 = (x + 3)(x + 1)

Answer 1

x^2 - 4x + 3 = (x - 3)(x - 1)

Reason: Factor 1 has +x and three negatives → (x - 3). Factor 2 has +x and one negative → (x - 1). Their product expands to x^2 - 4x + 3, matching the product tiles.