Question

eliott was trying to factor $6x^2 - 18$. he found that the greatest common factor of these terms was 6 and made an area model:
what is the width of eliotts area model?
width =

Explanation:

Step1: Recall area of rectangle formula

The area of a rectangle is \( \text{Area} = \text{length} \times \text{width} \). Here, the length is 6, and the area is \( 6x^2 - 18 \). We need to find the width, so we can use the formula \( \text{width} = \frac{\text{Area}}{\text{length}} \).

Step2: Substitute the values into the formula

Substitute the area \( 6x^2 - 18 \) and the length 6 into the formula:
\[
\text{width} = \frac{6x^2 - 18}{6}
\]

Step3: Simplify the expression

We can split the fraction:
\[
\text{width} = \frac{6x^2}{6} - \frac{18}{6}
\]
Simplify each term:
\[
\frac{6x^2}{6} = x^2 \quad \text{and} \quad \frac{18}{6} = 3
\]
So, the width is \( x^2 - 3 \).

Answer:

\( x^2 - 3 \)