Polynomials
Saturday, December 24th, 2011 at
6:35 pm
Polynomials
The following is a polynomial in x:
The polynomial is of degree n*, is the leading coefficient, and is the constant term.
* the exponent must be a positive integer.
Important Vocabulary:
1. polynomial – an algebraic expression a number of terms
2. coefficient – the number in front of the variable
3. degree – the power of a variable
4. monomial – a polynomial of only one term
5. binomial – a polynomial of two terms
6. trinomial – a polynomial of three terms
7. standard form – a polynomial written with descending powers of x
Examples: Standard Form Degree LC*
*LC – leading coefficient
Degree of a polynominal with more than 1 variable:
Degree of a term = sum of the exponents of the variables in the term
Degree of a polynomial = highest degree of its terms
Leading coefficient = coefficient of the highestdegree term
More Examples:
1. a polynomial of degree zero —
2. a trinomial of degree five —
3. a binomial with a leading coefficient of 2 —
4. a monomial of with a positive degree —
5. a trinomial with a leading coefficient of 2/3 –
6. a third degree polynomial with a leading coefficient of 1 —
Operations with Polynomials
Addition/Subtraction – sum/difference – put like terms together
Multiplication – products

Polynomial by polynomial

Special Products
Sum & Difference of same terms
Square of a binomial
Cube of a binomial
and
Factoring — writing a polynomial as the product of factors
For information about factoring go to the post called Factoring.
Filed under: Prerequisites for PreCalculus
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