Question

factoring a trinomial using a geometric model
use a geometric model to factor x² - 6x + 8 by following these steps:
step 1: model the trinomial by placing tiles in the product section to form a rectangle at the top left.

Explanation:

Step1: Analyze the trinomial coefficients

We have the trinomial $x^{2}-6x + 8$. We need to find two numbers that multiply to $8$ (the constant term) and add up to $-6$ (the coefficient of $x$).

Step2: Find the two - numbers

The pairs of factors of $8$ are: $(1,8)$ and $(2,4)$. Since $(-2)+(-4)=-6$ and $(-2)\times(-4) = 8$, the two numbers are $-2$ and $-4$.

Step3: Write the factored form

The factored form of $x^{2}-6x + 8$ is $(x - 2)(x - 4)$.

Answer:

$(x - 2)(x - 4)$