Polynomials Vocabulary (7.5)
Monomial – a number, variable, or product of numbers and variables with whole number exponents
Degree of a monomial – the sum of the exponents of the variables
7xy has degree 2 (1+1=2) because it’s really 7x1y1
4p4q3 has degree 7 (3+4=7)
12 has degree 0 (all constants are degree 0!) because it’s really 12x0 but x0=1 so we don’t have to write it
Polynomial – a monomial or the sum or difference of monomials
Examples:
3xy + 7
Non-examples:
4x2 – 5x – 2
9a 3
5x-4 + 2x
2b 3
4n3
17
Degree of a polynomial – degree of the term with the greatest degree
 because
11x7 + 3x3 is degree 7
2w2z + z4 – 5 is degree 4
5r – 6 is degree 1
11x7: degree 7
because 2w2z: degree 3
because
5r: degree 1
3x3: degree 3
z4: degree 4
5: degree 0
-6: degree 0
x3y + x2y3 – x4 + 2y is degree 5 because x3y: degree 4 x2y3: degree 5 –x4: degree 4 2y: degree 1
Standard form of a polynomial – polynomial that is written with the term in order from greatest degree to least
degree
6x – 7x5 + 4x2 + 9 is not in standard form  –7x5 + 4x2 +6x + 9 is in standard form
Leading coefficient – coefficient of the first term when the polynomial is written in standard form
–7x5 + 4x2 +6x + 9 has a leading coefficient of -7
y6 + y3 + 3y has a leading coefficient of 1 (because it’s really 1y6)
–x3 + 2x2 – 5x + 13 has a leading coefficient of –1 (because it’s really –1x3)
polynomials can be classified by the number of terms they have and/or their degree:
Number of terms
1
2
3
4 or more
Name
monomial
binomial
trinomial
polynomial
prefix
mono = 1
bi = 2
tri = 3
poly = many
degree
0
name
constant
1
2
3
4
5
6 or more
linear
quadratic
cubic
quartic
quintic
6th degree, 7th degree, etc.
like the word…
monopoly, monocle
bicycle, binary
tricycle, triplets
polymer, polygon
think of…
regular numbers are called constants (no variables – no variation – no
change)
linear functions looked like y = 5x – 2 and have regular x
quadratus is Latin for “square” – x2 finds area of a square
volume is measured in cubic units (x3)
4 quarters in a dollar, 4 quarts in a gallon
5 babies are called quintuplets