2. Know the basic definitions for polynomials.
Recall that any combination of variables or constants (numerical values) joined by
the basic operations of addition, subtraction, multiplication, and division (except
by 0), or raising to powers or taking roots is called an algebraic expression.
Polynomials are the simplest kind of algebraic expression.
3. Know the basic definitions for polynomials.
Polynomials are fundamental in algebra. Recall from Section previous lesson
that a term is a number, a variable, or the product or quotient of a number of
one or more variables raised to powers.
Examples of terms include:
Coefficients are written in blue.
4. Know the basic definitions for polynomials.
A polynomial containing only the variable x is called a polynomial in x.
A polynomial in one variable is written in descending powers of the variable if
the exponents on the variable decrease from left to right.
The powers of x are decreasing from left to right. We can think of this polynomial as
5. Some Common Polynomials
Polynomials having a specific number of terms are commonly given special names.
Trinomial = a polynomial with three terms
Binomial = a polynomial with two terms
Monomial = a polynomial with one term
6. The Degree of a Polynomial
The degree of a nonzero term with only one variable is the exponent on the
variable. The number 0 has no degree.
The degree of a polynomial is the highest degree of any of its nonzero terms.
10. GOALS
Enumerate the rules of adding and subtracting
polynomials
Add and subtract polynomials.
Work collaboratively with classmates in solving problems
11. Addition and Subtraction of Polynomials
Addition of polynomials is just a matter of adding up like terms. For example,
consider the following polynomials:
We can use the associative and commutative properties to rearrange the terms
and then we add the like terms.
14. Sec 6.2 - 14
Subtraction of Polynomials
To subtract B from A, we add the negative of B to A. Perform the indicated
subtractions.
15. Subtracting Polynomials
We can subtract these polynomials vertically by writing the first polynomial above the
second, lining up like terms in columns.
Change all the signs in the second polynomial and add.
