In the expression $3x$, what is the $3$?

Question

So this is quite a simple question. I KNOW I learnt this before, but can't for the life of me figure out or find anywhere that refers to the definition I'm looking for. Look at the expression $$ 3x $$ In this expression, what is the $3$ in this context? The $3$ 'prefixes' the $x$, but I don't believe that it is called a prefix of $x$.

Answer 1

It depends on the algebraic structure you have in mind and what $3x$ represents.

• If $3x$ represents the scalar multiplication of $3$ and $x$, then $3$ is a scalar and $x$ is a vector. But sometimes, the scalars are called coefficients, especially when they appear in linear combinations.
• The expression $3x$ could also represent the vector addition of $3$ and $x$ (for example, when the structure you have in mind is the vector space of positive-real numbers with usual multiplication and exponentiation), or it could be the inner product of $3$ and $x$ (in a one-dimensional inner-product space). In both cases, $3$ and $x$ are vectors.
• A more general term would simply be element. For example, if you have a group structue, and $3x$ represents the combination of $3$ and $x$ using the group operation, then $3$ and $x$ are elements of the group.

Answer 2

A "scalar" in contex of Algebra. Could be also a "coefficient".

Answer 3

You call it the coefficient of $x$, and it multiplies $x$.

You can also consider that $3$ is the multiplier of the multiplicand $x$, but this is more appropriate in symmetrical situations (like $ab$).