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Adding and Subtracting 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: 3x2 & −5 are two different terms. 3x2 − 5 is not a term (it is two

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: 3x2 − 4x − 2 & 4xy2 + 3x2 − 3y + x − 2 are polynomials.
Not Polynomials: & 3x-2 + 4x2 − 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 :

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



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

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:

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 −x3 + x2 − 3x + 5? ___________________

EXAMPLE: Perform the following operations

f.) Find the difference when 32x2 −17x + 45 is subtracted from the sum of

g.) (0.02x2 + x −.004) − (.01x2 + .0001x −.02)

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