Question

factoring a trinomial using a geometric model. 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 trinomial \(ax^{2}+bx + c\) (here \(a = 1\), \(b=3\), \(c = 2\)), we need to find two numbers that multiply to \(ac=1\times2 = 2\) and add up to \(b = 3\). The numbers are 1 and 2.

Step2: Write factored form

\(x^{2}+3x + 2=(x + 1)(x+2)\)

Answer:

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