Question

Four students were asked to write an expression which has terms that have a greatest common factor of 8c. The expressions provided by the students are shown below.


Tanya
32 c + 16 c d

Wyatt
8 c minus 48 c d

Xavier
36 c minus 24 c

Yang
8 c + 40

Which student wrote the correct expression?
Tanya
Wyatt
Xavier
Yang

Answer 1

To determine which student wrote an expression with terms that have a greatest common factor (GCF) of \(8c\), let's analyze each student's expression.

**1. Tanya's Expression:**
\[ 32c + 16cd \]
The GCF of \(32c\) and \(16cd\) is:
- For the numeric coefficients: GCF of \(32\) and \(16\) is \(16\).
- The variable part includes \(c\) (common in both terms).
Thus, the GCF of \(32c\) and \(16cd\) is \(16c\), not \(8c\).

**2. Wyatt's Expression:**
\[ 8c - 48cd \]
The GCF of \(8c\) and \(-48cd\) is:
- For the numeric coefficients: GCF of \(8\) and \(48\) is \(8\).
- The variable part includes \(c\) (common in both terms).
Thus, the GCF of \(8c\) and \(-48cd\) is \(8c\), which is correct.

**3. Xavier's Expression:**
\[ 36c - 24c \]
The GCF of \(36c\) and \(-24c\) is:
- For the numeric coefficients: GCF of \(36\) and \(24\) is \(12\).
- The variable part includes \(c\) in both terms.
Thus, the GCF of \(36c\) and \(-24c\) is \(12c\), not \(8c\).

**4. Yang's Expression:**
\[ 8c + 40 \]
The GCF of \(8c\) and \(40\) is:
- For the numeric coefficients: GCF of \(8\) and \(40\) is \(8\).
- The variable part includes \(c\) in only one term.
Thus, the GCF of \(8c\) and \(40\) is \(8\), but it does not include \(c\), so it is not \(8c\).

Based on the analysis, the only student whose expression has a GCF of \(8c\) is **Wyatt**.