Question

luca writes (9y + 3) as a product of the gcf and the remaining factors. what mistake does luca make?
a) he writes 3 outside the parentheses.
b) he writes the term (9y) as (3 cdot 3y).
c) he writes the term 3 as (3 cdot 3).
d) he finds 3 as the gcf of (9y) and 3.

Explanation:

Step1: Recall GCF factoring

To factor \(9y + 3\) using GCF, first find GCF of \(9y\) and \(3\). GCF of \(9y\) (which is \(3\times3y\)) and \(3\) (which is \(3\times1\)) is \(3\). Then, we write as \(3(3y + 1)\).

Step2: Analyze each option

• Option 1: Writing \(3\) outside parentheses is correct (part of factoring out GCF), so not a mistake.
• Option 2: Writing \(9y\) as \(3\cdot3y\) is correct (since \(3\times3y = 9y\)), not a mistake.
• Option 3: Writing \(3\) as \(3\cdot3\) is wrong. Because \(3\times3=9\), but \(3 = 3\times1\), not \(3\times3\). This is an error in representing \(3\) when factoring.
• Option 4: Finding GCF of \(9y\) and \(3\) as \(3\) is correct, not a mistake.

Answer:

He writes the term 3 as \( 3 \cdot 3 \). (The option with "He writes the term 3 as \( 3 \cdot 3 \).")