Answer:
The expression is always divisible by 9.
Step-by-step explanation:
Let is call [tex]x[/tex] the number with which the expression [tex]15p -6p[/tex], then
[tex]\dfrac{15p-6p}{x}[/tex]
must give an integer.
Simplifying the numerator, we get:
[tex]\dfrac{9p}{x}[/tex]
Now, this tells us that when [tex]x= 9[/tex], the the expression will always give an integer [tex]p[/tex]:
[tex]\dfrac{9p}{9} =p;[/tex]
therefore, the expression [tex]15p-6p[/tex] will always be divisible by 9.
