# Adding and Subtracting Polynomials

**Polynomials:
**A term is defined as an expression containing a constant or the product of a

constant and one or more variables. Any term is made up of a number part

and a variable part .

Terms: 3x^{2} & −5 are two different terms. 3x^{2} − 5 is not
a term (it is two

terms).

A Polynomial is defined as a single term or the sum of two
or more terms

containing only whole number exponents on its variables.

Polynomials: 3x^{2} − 4x − 2 & 4xy^{2} + 3x^{2} − 3y + x − 2 are
polynomials.

Not Polynomials:
& 3x^{-2} + 4x^{2} − 2 are not polynomials.

A monomial is a polynomial with one term, a binomial is a polynomial with

two terms , and a trinomial is a polynomial with three terms.

Give an example of a: Monomial:

Binomial :

Trinomial :

The **degree of a term** is the sum of the exponents on the variables.

Term:

Degree:

The** degree** of a polynomial is determined by the term with the largest

degree.

**EXAMPLE:** Determine the degree of the following polynomials:

A polynomial that is written in standard form will have its terms written so the

exponents will be in descending powers .

**EXAMPLE:** Write the polynomial in standard form:

** COMBINING LIKE TERMS (Review)
**To add two objects, they must be of the same units. We can’t add feet and

inches because they don’t match. The same goes for terms. They must be

like terms .

To add two like terms :

Combine their _______________, and leave the ____________part alone.

How do we combine unlike terms ? _________________

What is the opposite of −x^{3} + x^{2} − 3x + 5? ___________________

** EXAMPLE:** Perform the following operations

f.) Find the difference when 32x^{2} −17x + 45 is subtracted
from the sum of

g.) (0.02x^{2} + x −.004) − (.01x^{2} + .0001x −.02)

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