Question

the trinomial $x^2 - 3x - 4$ is represented by the model. what are the factors of the trinomial? $\circ$ $(x + 1)$ and $(x - 4)$ $\circ$ $(x + 4)$ and $(x - 1)$ $\circ$ $(x + 5)$ and $(x - 4)$ $\circ$ $(x + 4)$ and $(x - 5)$

Explanation:

Step1: Identify $a, b, c$ for $ax^2+bx+c$

For $x^2 - 3x - 4$, $a=1$, $b=-3$, $c=-4$

Step2: Find two numbers with product $ac$, sum $b$

Need numbers: product $1\times(-4)=-4$, sum $-3$. These are $1$ and $-4$.

Step3: Rewrite and factor by grouping

$$\begin{align*} x^2 - 3x - 4&=x^2 + x - 4x - 4\\ &=x(x+1) - 4(x+1)\\ &=(x+1)(x-4) \end{align*}$$

Answer:

$(x + 1)$ and $(x - 4)$