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

1 Answer
Azimet
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.

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