Answered

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Which algebraic expression is a product with a factor of 5?

A. [tex]\(5(y-6)\)[/tex]
B. [tex]\(-2y + 5 + 3\)[/tex]
C. [tex]\(3y + 1\)[/tex]
D. [tex]\(5y - 7\)[/tex]

Sagot :

GinnyAnswer
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]
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