Question

modeling polynomials with algebra tiles
which geometric model using algebra tiles represents the factorization of x² - 5x + 6?

Explanation:

Step1: Factor the polynomial

We factor \(x^{2}-5x + 6\) using the formula for factoring quadratic polynomials \(ax^{2}+bx + c\) (\(a = 1\), \(b=-5\), \(c = 6\)). We need to find two numbers that multiply to \(ac=6\) and add up to \(b=-5\). The numbers are \(-2\) and \(-3\) since \((-2)\times(-3)=6\) and \(-2+( - 3)=-5\). So \(x^{2}-5x + 6=(x - 2)(x - 3)\).

Step2: Interpret algebra - tiles

In algebra - tile models, a square tile represents \(x^{2}\), a long rectangular tile represents \(x\), and a small square tile represents \(1\). The factored form \((x - 2)(x - 3)\) means we have a rectangle with dimensions \((x-2)\) and \((x - 3)\). The area of the rectangle is made up of one \(x^{2}\) - tile, \((2 + 3)=5\) negative \(x\) - tiles, and \(2\times3 = 6\) positive unit tiles.

Answer:

The geometric model that has one large square (representing \(x^{2}\)), five long - rectangular tiles with the negative side showing (representing \(-5x\)) and six small square tiles with the positive side showing (representing \(+6\)) is the correct one. Without seeing the specific options clearly, based on the above - described structure of tiles, you can identify the correct model among the given choices.