Question

the model of a trinomial is shown. what are the factors of the trinomial? select two options. \\(\square x - 14\\) \\(\square x + 7\\) \\(\square x - 7\\) \\(\square x - 2\\) \\(\square x + 2\\)

Explanation:

Step1: Identify the trinomial

Count each tile:
$+x^2 + 2x - 14$ (7 negative units in row 2 + 7 negative units in row 3 = 14 negative units; 2 positive $x$ tiles; 1 positive $x^2$ tile)

Step2: Factor the trinomial

Find two numbers that multiply to $1\times(-14)=-14$ and add to $2$. The numbers are $7$ and $-2$.
Rewrite and factor by grouping:

$$\begin{align*} x^2 + 2x -14&=x^2 +7x -2x -14\\ &=x(x+7)-2(x+7)\\ &=(x+7)(x-2) \end{align*}$$

Answer:

B. $x + 7$
D. $x - 2$