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$15x{y}^2$.

Short answer

The given sentence isTrue.

Step-by-step solution

Step 1. Find the greatest common factor of 10x and 15xy2.

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.