Download Degree of the polynomial

Polynomial definitions
Algebraic expression -numbers and/or variables with
operations
2a + 4 3r 6y 7
term: numbers or variables separated by a + sign in an
algebraic expression
Polynomial
polynomial- an expression with more than two terms
3x4 + 2x + 1
4x4 + 2x3 + 2x + 1
A. Classified by Number of Terms
1.) monomial: an expression that is a constant, a variable or the
product of both with variables having whole number exponents (an
expression with one term)
4x2 -7ab -8 2x3y
2.) binomial - an expression with two terms
5y + 3 3b2 - 9a
3.) trinomial - a polynomial with three terms
3x4 + 2x +1 2w3 + 6w - 9
*greater than three terms does not have a special name
Place the polynomials in the correct box
Monomial
2x
3y2
9
binomial
y+1
trinomial
y2 + y - 7
y3 + 6
3w4 + 12
x3 - x2 - x
Degree
Degree of each term - the exponent of the variable
Degree of the polynomial - the largest degree of its terms
B. Classified by degree
1.)constant - a monomial that is a numeral;
an expression that does not have a variable
4 7 21 67
2.) Linear- a term or polynomial with the variable raised to the first power
4x 6y 34t w + 34
3.) Quadratic- a term or polynomial with the variable raised to the second powe
2x2 3y2 + 7
4.) Cubic a term or polynomial with the variable raised to the third power
7x3 -5y3 + 9
5.) quartic- a term or polynomial with the variable raised to the fourth power
9y4 + 4
constant
8
Linear
5y
6y + 2
8k + 23
Quadratic
Cubic
9q2 + 9q
m + 3m3 + 9m2
Standard Form: terms of the polynomial are in descending order (largest degree down to the
smallest degree)
Ex:
Write the following in standard form.
Leading coefficient the coefficient of the term with the largest degree in the polynomial
Identify the leading coefficient.
1.) 3x2 + x + 4
2.) x + 5
3.) 7x2 + 2x5 + 4x
Addition and Subtraction of Polynomials
A: Addition (Combining Like Terms):
ex 1: (-8x2 + x + 2) + ( 8x2 - 2x + 4)
ex 2: (6y2 - y + 3) + ( -2y + y2 - 7)
B: Subtraction ( Distribute -1 and then combine like terms):
ex 1: (-6x3 + 5x - 30) - ( 2x3 +4x2 - 3x + 1)
ex 2: (12x - 8x2 + 6) - ( -8x2 - 3x + 4)