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Add - Subtract POLYNOMIALS

A monomial is an algebraic expression that is a product of a real number and one or more letters with
whole number exponents . A polynomial is an algebraic sum of monomials. Special names are given
to polynomials of one, two and three terms ( monomial, binomial, trinomial ) and all others are simply
called polynomial. The degree of a polynomial in one variable is the highest power to which the
variable is raised. Polynomials of degree 2 are frequently called “quadratic” and polynomials of
degree 3 are called “cubic”.

The degree of a monomial in several variables is the sum of the exponents of each variable. The
degree of a polynomial in several variables is the highest degree of the monomials in the polynomial.

Examples:
Monomials:
2, [degree 0], 3a, [degree 1], , [degree 3], , [degree 4], , [degree 5]
Binomials : [degree 2], [degree 2], 3a – 6 [degree 1], [degree 3]
Trinomials : [degree 2], [degree 9]

Addition of Polynomials : To add two or more polynomials use the basic properties (associative,
commutative, distributive, etc.) and add the coefficients of like terms (or combine like terms .)

Caution: Like terms must have the same letters with the same exponents. Do not change exponents when
you add polynomials.
If you can’t combine terms in a polynomial before adding polynomials, you can’t combine them after adding.

Examples:

 
Apply the associative and commutative properties
Apply the distributive property.
Add coefficients.
Watch signs and note that the middle terms aren’t “similar”.
Apply the associative and commutative properties.
Apply the distributive property.
Add coefficients.

Negation of a Polynomial: To negate a polynomial multiply each term by (-1).

Example:

Subtraction of Polynomials : To subtract a polynomial from another you must add the “opposite”
(or negate the polynomial following the “minus sign” and add the result algebraically).

Watch the signs.
Change to (-1) times polynomial
Distribute the (-1) over the 2nd polynomial.
Apply the associative and commutative properties.
Add coefficients.
Watch the signs.
Change to (-1) times polynomial.
Distribute the (-1) over the 2nd polynomial.
Apply associative and commutative properties.
Add coefficients.
Note that the middle terms aren’t “similar”.
Watch the signs. Change to (-1) times polynomial.
Distribute the (-1) over the 2nd polynomial.
Apply the associative and commutative properties.
Apply the distributive property.
Add coefficients.
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