Question

If x is an integer, which of the following cannot have 4 as a factor?

a) 2x
b) 3x
c) 4x
d) 5x

Answer 1

The expression b) 3x cannot have 4 as a factor because 3 is not a multiple of 4, and without x containing a factor of 4, the product 3x cannot have 4 as a factor.

Step-by-step explanation:

If x is an integer, the expression 3x cannot have 4 as a factor because 3 is not a multiple of 4 and cannot contribute to a product that has 4 as a factor unless x itself contains a factor of 4. Looking at the others:

• 2x can have 4 as a factor if x is an even integer, as multiplying by 2 will increase it by a factor of two.
• For 4x, since 4 is already a factor, any integer x will preserve that 4 as a factor in the product, effectively increasing it by a factor of four.
• Similarly, 5x can also have 4 as a factor if x itself is a multiple of 4. Multiplying by 5 does not influence whether 4 is a factor.

Thus, 3x is the expression which cannot have 4 as a factor unless x itself contains a factor of 4.