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.
step 3: what is the factored form of this trinomial?
○ ((x + 2)(x + 1))
○ ((x + 3)(x + 2))
○ ((x + 3)(x + 1))
the correct tiles are now in place.
check

Explanation:

Step1: Recall factoring trinomials

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 \(x\)).

Step2: Find the numbers

The numbers \(2\) and \(1\) multiply to \(2\) (\(2\times1 = 2\)) and add up to \(3\) (\(2 + 1=3\)).

Step3: Write the factored form

Using these numbers, we can factor the trinomial as \((x + 2)(x + 1)\) because when we expand \((x + 2)(x + 1)\) using the distributive property (FOIL method):
\[

$$\begin{align*} (x + 2)(x + 1)&=x\times x+x\times1+2\times x + 2\times1\\ &=x^2+x + 2x+2\\ &=x^2+3x + 2 \end{align*}$$

\]
Which matches the given trinomial.

Answer:

A. \((x + 2)(x + 1)\)