Question

use a geometric model to factor ( x^2 - 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.
step 2: drag tiles to the sections labeled factor 1 and factor 2 to represent the factors.

Explanation:

Step1: Recall factoring trinomial \(ax^2 + bx + c\)

For \(x^2 - 6x + 8\), we need two numbers that multiply to \(8\) and add to \(-6\). The numbers are \(-2\) and \(-4\) since \((-2)\times(-4)=8\) and \((-2)+(-4)=-6\).

Step2: Write the factored form

Using the geometric model (area of rectangle), the trinomial \(x^2 - 6x + 8\) factors as \((x - 2)(x - 4)\). We can verify by expanding: \((x - 2)(x - 4)=x^2-4x-2x + 8=x^2-6x + 8\), which matches the original trinomial.

Answer:

The factored form of \(x^2 - 6x + 8\) is \((x - 2)(x - 4)\)