Using Algebra Tiles to Factor Polynomials

Algebra tiles are a visual way to represent polynomials with shapes: a large square for x², a rectangle for x, and a small square for the constant 1. Laying out tiles for a polynomial turns an abstract expression into something you can see and rearrange.

To model x² + 3x + 2: lay out 1 large square tile (for x²), 3 rectangular tiles (for the 3x), and 2 small unit tiles (for the +2). The total collection of tiles represents the polynomial exactly, term by term, building on the idea of what a polynomial is.

Tiles are especially useful for factoring: arrange the x², x, and unit tiles into a rectangle, and the rectangle's side lengths are the two factors. For x² + 3x + 2, arranging the tiles into a rectangle gives sides of (x + 1) and (x + 2) — the same result you'd get from factoring by grouping, but built visually instead of algebraically.

Algebra tiles make the connection between multiplying and factoring concrete: multiplying two binomials builds a rectangle from tiles, and factoring means finding the rectangle's side lengths from a given tile collection. This visual model reinforces the same rules used in multiplying binomial by binomial.

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