Question

What is the coefficient in the expression `5a^2-7`?

Answer 1

`5`

Explanation:

A `color(red)("coefficient")` is a number that is multiplied with a variable. In this example, `5` is multiplied with `a^2` so `5` is a coefficient.

In addition, the `-7` in this expression is called a `color(red)("constant")`, which is a number NOT multiplied by a variable. There is usually one constant in an expression but there can be multiple coefficients depending on the variables and their degrees (or powers, e.g `x, x^2, x^3,...`)

ex: `5x^2+2x+4`

Here the constant is `4` and there are two coefficients: `5` and `2` but only `5` is what is known as the `color(red)("leading coefficient")` which is the coefficient being multiplied by the variable with the highest degree (In this case: `x^2` has a higher degree than `x`)