Certainly! Let's go through the problem step-by-step to determine the width of Yun's area model:
1. Identify the given polynomial: We start with the expression [tex]\( 7x^2 - 14x \)[/tex].
2. Determine the greatest common factor (GCF): Yun found that the GCF of the two terms [tex]\( 7x^2 \)[/tex] and [tex]\( -14x \)[/tex] is [tex]\( 7x \)[/tex].
3. Factor out the GCF from the polynomial: When we factor [tex]\( 7x \)[/tex] out of [tex]\( 7x^2 - 14x \)[/tex], we get:
[tex]\[
7x^2 - 14x = 7x(x - 2)
\][/tex]
4. Interpret the area model: In an area model, the polynomial expression is represented as a product of two factors: the GCF and the remaining binomial. The width of the area model corresponds to the GCF that was factored out.
5. Extract the width: Given that the GCF is [tex]\( 7x \)[/tex], the numerical part (without the variable [tex]\( x \)[/tex]) of the width in this context is just [tex]\( 7 \)[/tex].
Considering Yun's area model:
[tex]\[
\begin{array}{lll|l}
7x & 7x^2 & -14x
\end{array}
\][/tex]
The width of Yun’s area model is:
[tex]\[
\boxed{7}
\][/tex]
So, the width of Yun's area model is [tex]\( 7 \)[/tex].
