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.
step 3: what is the factored form of this trinomial?
( \bigcirc (x - 2)(x - 4) )
( \bigcirc (x + 2)(x - 4) )
( \bigcirc (x - 8)(x + 1) )
( \bigcirc (x - 8)(x - 1) )
correct!
check

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 - 6x + 8\), we need two numbers that multiply to \(8\) (the constant term) and add up to \(-6\) (the coefficient of the \(x\)-term).
The pairs of factors of \(8\) are: \(1\) and \(8\), \(2\) and \(4\).
Since the middle term is \(-6x\) and the constant term is positive, both numbers should be negative.
\(-2\) and \(-4\) multiply to \(8\) (\((-2)\times(-4)=8\)) and add up to \(-6\) (\(-2 + (-4)=-6\)).

Step2: Write the factored form

Using these numbers, we can factor the trinomial as \((x - 2)(x - 4)\) because when we expand \((x - 2)(x - 4)\) using the distributive property (FOIL method):
\[

$$\begin{align*} (x - 2)(x - 4)&=x\times x - 4x - 2x + (-2)\times(-4)\\ &=x^2 - 6x + 8 \end{align*}$$

\]
Which matches the original trinomial.

Answer:

A. \((x - 2)(x - 4)\)