To determine which expression is equivalent to the polynomial [tex]\( 60x - 5 \)[/tex], let's carefully factor out any common factor from the given polynomial and then compare it to the given options.
Starting with the given polynomial:
[tex]\[ 60x - 5 \][/tex]
We notice that both terms [tex]\( 60x \)[/tex] and [tex]\( -5 \)[/tex] are divisible by 5. Therefore, we can factor out 5 from the entire expression:
[tex]\[ 60x - 5 = 5(12x - 1) \][/tex]
Now, we need to determine how we can format this into one of the given choices. The goal is to get it into a form that resembles:
[tex]\[ k(m x + n) \][/tex]
where [tex]\( k \)[/tex], [tex]\( m \)[/tex], and [tex]\( n \)[/tex] are integers.
Examining the choices, none of them follow the exact simplification we performed above. Realizing this, we'll do a check on each given option by distributing the factors inside the parenthesis to see if we can match [tex]\( 60x - 5 \)[/tex]:
1. [tex]\( 10(6 = -5) \)[/tex]
This does not make sense mathematically as [tex]\( 6 = -5 \)[/tex] is not equivalent.
2. [tex]\( 10(3 = -5) \)[/tex]
This also does not make sense mathematically as [tex]\( 3 = -5 \)[/tex] is not equivalent.
3. [tex]\( 10(6x - 50) \)[/tex]
Distributing the 10 inside the parentheses:
[tex]\[ 10 \cdot 6x - 10 \cdot 50 = 60x - 500 \neq 60x - 5 \][/tex]
Thus, this option is incorrect.
4. [tex]\( 8(30 = -5) \)[/tex]
Again, this does not make sense mathematically as [tex]\( 30 = -5 \)[/tex] is not equivalent.
None of the given choices match directly.
This suggests there might be an issue with interpreting the choices. Upon close reading, this particular choice:
[tex]\[ 10(6x - 50) \][/tex]
appears to have been potentially miswritten and might be intended as a normal single distribution term after all like indicated.
Thus, none of the choices match directly. Factoring the polynomial into the suitable factored expression could lead to:
[tex]\[ 10(6x - 0.5) \][/tex]
But this isn't listed - suggesting errors in options or approach.
Final Answer:
Revisit your provided polynomial options; correct path mathematically explores through [tex]\( 5(12x-1)\)[/tex].
