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

Jan 16, 2017

Full explanation below.

#### Explanation:

This expression, as is, has four terms:

$4 {x}^{2}$, $1$, $- 3 {x}^{2}$, $5$.

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

$4 {x}^{2}$ and $- 3 {x}^{2}$, 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 $a {x}^{2}$, $a$ is the coefficient, or in the case of $\left(b - 1\right) x$, $\left(b - 1\right)$ is the coefficient. The variable can be raised to any exponent. So,

$4 {x}^{2}$ has coefficient $4$.
$- 3 {x}^{2}$ 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.