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

1 Answer
Jan 16, 2017

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.