Question

the factorization of a trinomial is modeled with algebra tiles. which trinomial is factored? $\circ\\ x^2 + 3x - 6$ $\circ\\ x^2 + 5x - 6$ $\circ\\ x^2 + 3x - 2$ $\circ\\ x^2 + x - 6$

Explanation:

Step1: Count total $x^2$ tiles

There is 1 positive $x^2$ tile: $+x^2$

Step2: Count total $x$ tiles

Positive $x$ tiles: $+x, +x, +x, +x, +x$ (5 total: $+5x$)
Negative $x$ tiles: $-x, -x$ (2 total: $-2x$)
Combine: $5x - 2x = +3x$

Step3: Count constant tiles

Negative constant tiles: $-1$ (8 total: $-8$? No, wait: top row 2, middle row 2, bottom 2 rows 2 each: 2+2+2+2=8? No, wait, no—wait the side and top are factors. Wait, the factors are $(x+3)$ (left column: $+x, +1, +1, +1$) and $(x-2)$ (top row: $+x, -1, -1$). Multiply them:
$(x+3)(x-2) = x^2 -2x +3x -6 = x^2 +x -6$. Wait, no, let's count the tiles inside:
$x^2$, then $x$ tiles: $+x$ (top), $+x, +x, +x$ (bottom 3), $-x, -x$ (middle right): total $x$: $1+3-2=+1x$. Constants: top right 2 negatives, middle right 2, bottom right 4: total 8? No, no, the algebra tile rectangle's area is the trinomial. The length and width are the factors: left side is $x + 3$ (1 $x$ tile, 3 $+1$ tiles), top is $x - 2$ (1 $x$ tile, 2 $-1$ tiles). Multiply the factors:

Step1: Identify binomial factors

Left edge: $x + 3$, Top edge: $x - 2$

Step2: Expand using FOIL method

$(x+3)(x-2) = x^2 -2x +3x -6$

Step3: Combine like terms

$x^2 + (-2x+3x) -6 = x^2 +x -6$

Answer:

$x^2 + x -6$ (the fourth option)