Question

use a geometric model to factor ( x^2 + 3x + 2 ) by following these steps:
step 1: model the trinomial by placing tiles in the product section to form a rectangle at the top left. the ( x^2 ) tile is already in the correct place.
step 2: drag tiles to the sections labeled factor 1 and factor 2 to represent the factors.

Explanation:

Step1: Recall factoring trinomial

To factor \(x^2 + 3x + 2\), we need two numbers that multiply to \(2\) (the constant term) and add up to \(3\) (the coefficient of \(x\)). The numbers are \(1\) and \(2\) since \(1\times2 = 2\) and \(1 + 2=3\).

Step2: Write the factored form

Using the numbers from Step 1, the trinomial \(x^2+3x + 2\) factors as \((x + 1)(x + 2)\). In the geometric model (area model), the length and width of the rectangle (representing the factors) should be \(x + 1\) and \(x + 2\) such that the area (product) is \(x^2+3x + 2\). So, Factor 1 should be \(x + 2\) and Factor 2 should be \(x + 1\) (or vice versa, depending on the model's orientation). When we place the tiles, the \(x^2\) tile is at the top - left, then we have \(x\) tiles and unit tiles. The number of \(x\) tiles in one factor's row and the other factor's column should correspond to the coefficients in the factored form.

Answer:

The factored form of \(x^2 + 3x + 2\) is \((x + 1)(x + 2)\), so in the geometric model, Factor 1 can be \(x + 2\) and Factor 2 can be \(x + 1\) (or the other way around depending on the model's setup) to represent the factors.