To determine which algebraic expression has a factor of 5, let's analyze each option:
Option A: [tex]\( 5(y - 6) \)[/tex]
This expression is a product where [tex]\( 5 \)[/tex] is multiplied by [tex]\( (y - 6) \)[/tex]. Clearly, [tex]\( 5 \)[/tex] is a factor of this expression.
Option B: [tex]\( -2y + 5 + 3 \)[/tex]
This expression can be simplified by combining like terms:
[tex]\[ -2y + 5 + 3 = -2y + 8 \][/tex]
Here, [tex]\( -2y + 8 \)[/tex] does not have a factor of [tex]\( 5 \)[/tex].
Option C: [tex]\( 3y + 1 \)[/tex]
This expression is already simplified and does not have [tex]\( 5 \)[/tex] as a factor.
Option D: [tex]\( 5y - 7 \)[/tex]
This expression shows [tex]\( 5 \)[/tex] multiplied by [tex]\( y \)[/tex] (since [tex]\( 5 \)[/tex] is the coefficient of [tex]\( y \)[/tex]). Therefore, [tex]\( 5 \)[/tex] is a factor.
So, the expressions with a factor of 5 are:
- Option A: [tex]\( 5(y - 6) \)[/tex]
- Option D: [tex]\( 5y - 7 \)[/tex]
The number of algebraic expressions with a factor of 5 is:
[tex]\[ \boxed{2} \][/tex]
