Question

sort the expressions.
z
factors of 12z
12
factors of 7(z + 1)
7

Explanation:

Step1: Analyze \(12z\) factors

A factor of \(12z\) is a term that multiplies to give \(12z\). The expression \(12z = 12\times z\), so \(z\) is a factor of \(12z\). We place \(z\) in the "Factors of \(12z\)" box.

Step2: Analyze \(7(z + 1)\) factors

The expression \(7(z + 1)=7\times(z + 1)\), and we already have \(7\) in its box. The other factor is \((z + 1)\), but the given tile is \(z\) which doesn't match \((z + 1)\), so \(z\) belongs to \(12z\)'s factors. Also, \(12\) is a factor of \(12z\) (as \(12z=12\times z\)), and \(7\) is a factor of \(7(z + 1)\) (as \(7(z + 1)=7\times(z + 1)\)). Now, for the tile \(z\), since \(12z = 12\times z\), \(z\) is a factor of \(12z\), so we move \(z\) to the "Factors of \(12z\)" box.

Answer:

• Move the tile \(z\) to the "Factors of \(12z\)" box (along with \(12\)). The "Factors of \(7(z + 1)\)" box has \(7\) and will later have \((z + 1)\) if that tile was present, but with the given tiles, \(z\) goes to "Factors of \(12z\)".