Q3. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined phrase or expression to make a true sentence.

$\underset{¯}{5x}$ is the greatest common factor of $10x$ and $15x{y}^2$.

Step-by-Step Solution

Answer

The given sentence is True.

Step 1. Find the greatest common factor of 10 x and 15 x y 2 .

Find the factorization of $10x$ and $15x{y}^2$.

$$\begin{gathered} 10x=2\cdot 5\cdot x \\ 15x{y}^2=3\cdot 5\cdot x\cdot y\cdot y \end{gathered}$$ 

Therefore, it can be noticed that:

The greatest common factor of $10x$ and $15x{y}^2$ is $5\cdot x$ or $5x$.

Step 2. State whether the given sentence is true or false.

The greatest common factor of $10x$ and $15x{y}^2$ is $5x$.

Therefore, the given sentence is True.