1/19-20
Tu/W
Introduction to Polynomials
monomial - a constant or a product of a constant and any quantity of variables.
exponents must be whole numbers (0,1,2,3,...)
degree of a monomial - the sum of all the exponents of the variables.
monomial
degree
6 -7 5x -4x3 2x2y4 -6x5y2z
0 0 1 3
6
8
polynomial - a sum or difference of any number of monomials.
degree of a polynomial - the degree of the highest degree monomial in the polynomial
not polynomials:
rational exponents
square roots
variables in denominator/ exponential functions/
negative exponents
x in the exponent
polynomial names
one term:
monomial
two terms:
binomial
three terms:
trinomial
four or more: polynomial
polynomial
standard form
degree names
degree 0:
constant
degree 1:
linear
degree 2:
quadratic
degree 3:
cubic
degree 4:
quartic
degree 5:
quintic
degree 6:
6th degree
degree
lead
coefficient
3
0
2
1
2
3
2
5
6
-7
25
5
-4
-3
7
9
2
7
-1
name by
degree
name by
# of terms
cubic
polynomial
constant
monomial
quadratic
binomial
linear
binomial
quadratic
trinomial
cubic
polynomial
quadratic
binomial
quintic
trinomial
6th degree
trinomial
Evaluating Polynomials
(a) evaluate f(x) for x = -3
(b) evaluate p(x) for x = -2
Adding & Subtracting Polynomials (combining like terms)
3x2 - 6x + 20 - (20x2 + 14x - 11)
-4x2 + 5x - 13 - (-6x2 - x + 8)
3x2 - 6x + 20 - 20x2 - 14x + 11
-4x2 + 5x - 13 + 6x2 + x - 8
-17x2 - 20x + 31
2x2 + 6x - 21
Factoring - Sum & Difference of Cubes