Question

How do you identify the terms, like terms, coefficients, and constant terms of the expression `4x^2 + 1 - 3x^2 +5`?

Answer 1

Full explanation below.

Explanation:

This expression, as is, has four terms:

`4x^2`, `1`, `-3x^2`, `5`.

The "like" terms, are the terms with the same exponent (power) on the variable, which we can add up. They are:

`4x^2` and `-3x^2`, which could, if we wanted, be added up to get `x^2`.

We could also call `1` and `5` "like terms", since they can be added up to get `6`.

A coefficient is the constant part of a product between constant and variable, in one term. So for example, when you have `ax^2`, `a` is the coefficient, or in the case of `(b-1)x`, `(b-1)` is the coefficient. The variable can be raised to any exponent. So,

`4x^2` has coefficient `4`.
`-3x^2` has coefficient `-3` (the minus sign is included)

Finally, constant terms are terms without a variable. So, the constants in this case are `1` and `5`.

If we wanted to add up the like terms to simplify the expression, it would be:

`x^2 + 6`, just for reference.