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Chapter Eleven — Polynomials
The Humongous Book of Algebra Problems
238
Classifying Polynomials
Labeling them based on the exponent and total terms
11.1 Classify the polynomial 7x + 10 according to its degree and the number of
terms it contains.
The degree of a polynomial is the highest exponent to which the variable in that
polynomial is raised. The only variable present in this expression is x, so the
polynomial has degree one. Such polynomials are described as linear.
The polynomial contains two terms, 7x and 10, so it is a linear binomial.
11.2 Classify the polynomial 6x
2
according to its degree and the number of terms it
contains.
The polynomial 6x
2
consists of a single term, so it is a monomial. That term
contains a variable raised to the second power, which classiﬁes the polynomial
11.3 Classify the polynomial –3x
2
+ 5x according to its degree and the number of
terms it contains.
The polynomial –3x
2
contains two terms: –3x
2
and 5x. Of those terms, the
highest power of x is 2, so the polynomial has degree two. A polynomial with
two terms and degree two is called a quadratic binomial.
11.4 Classify the polynomial 12x
3
according to its degree and the number of terms
it contains.
This polynomial consists of a single term, so it is a monomial. Furthermore, the
polynomial has degree three, which means it is cubic. In conclusion, 12x
3
is a
cubic monomial.
Note: Problems 11.5–11.6 refer to the polynomial 4x
2
– 7x + 6.
11.5 Classify the polynomial according to its degree and the number of terms it
contains.
This polynomial contains three terms (4x
3
, –7x, and 6) and has degree two
(because the highest power of x is two). Therefore, 4x
2
– 7x + 6 is a quadratic
trinomial.
It doesnt
have degree
one because
theres only one
variable. It has
degree one because
the only variable
there is raised
to the rst
POWER.
It’s a BInomial
because it has
TWO terms (bi =
two). A MONOmial
has ONE term, and
a TRInomial has
THREE terms.
RULE
OF THUMB:
The degree is
the highest power
of the variable.
Heres how polynomial
classications break
down by degree:
Degree 1: Linear