Question

use a geometric model to factor x² + 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 x² tile is already in the correct place.

Explanation:

Step1: Recall factoring concept

We know that for a quadratic trinomial \(ax^{2}+bx + c\) (here \(a = 1\), \(b=3\), \(c = 2\)), we want to find two numbers \(m\) and \(n\) such that \(m + n=b\) and \(m\times n=c\).

Step2: Find two - numbers

We need two numbers that add up to 3 and multiply to 2. The numbers are 1 and 2 since \(1+2 = 3\) and \(1\times2=2\).

Step3: Write the factored form

The factored form of \(x^{2}+3x + 2\) is \((x + 1)(x+2)\). In terms of the geometric model, we can think of the area of a rectangle with sides \((x + 1)\) and \((x + 2)\) representing the trinomial \(x^{2}+3x + 2\).

Answer:

\((x + 1)(x + 2)\)