Luttrell 2012
81
Name: ______________________
Date: _____
5h – Polynomials and Variation
Polynomials are algebraic e
x
pressions that involve only the operations of addition, subtraction,
and multiplication of variables. E
x
amples of polynomials are 3, 3
x
, 3
x
+ 1, 3
x
2
+ 6
x
+1, and
x
3
+
x
. Polynomials are described by the number of terms in the e
x
pression. Special names are
used for one-term through three-termed polynomials: monomial, binomial, trinomial.
Polynomials are also described by the highest-degree term in the e
x
pression: constant (zero-
degree), linear (first-degree), quadratic, cubic, quartic, quintic, he
x
tic (se
x
tic), heptic (septic), any
higher degrees are labeled by the ordinal value.
Match the following polynomials. If it isn’t a polynomial, e
x
plain wy:
___ A. 3
x
2
+ 6
x
+1
1. Quadratic trinomial
___ B. 3
x
2
+ 8x
4
2. Quintic monomial
___ C.
3
4
x
+
3. Non-polynomial; since ________________
___ D. 3
x
5
4. Non-polynomial, since division by variable
___ E. 5
5. He
x
tic binomial
___ F. 2
3
x
5
+
x
4
+ 3
6. Quartic binomial
___ G.
x
6
+
x
4
7. Constant
___ H.
8
4
x
+
8. Quintic trinomial
Ever had such a conversation?
“This recipe calls for eggs and flour.”
“How much flour?”
“One egg is needed for every cup of flour.”
The first statement tells what is needed, a simple list of ingredients. The third statement gives
the proportion of each amount. E
x
pressing how variables relate in an equation is very similar.
In the following exercises, you’ll get a chance to symbolically express that relationship of
variables. In the first couple of examples, you see the use of k. This letter represent the
proportion; its value is of secondary importance to the actually relationship of the variables. As
noted in the dialogue, the most important was getting the ingredients and then the proportion.
9.
y
varies directly with
x
.
(answer:
y
= k
x
)
10.
y
varies indirectly with
x
. (
y
= k/
x)
11.
y
varies with the reciprocal of
x
.
12.
y
varies with the cube of
x
.
13.
y
varies with the square root of
x
.
14.
y
is a constant.
15.
y
varies linearly with
x
.
16.
y
varies inversely with
x
.
17. Solve: The number of pounds you weigh is directly proportional to the number of kilograms you are.
Sally steps onto a scale calibrated in kilograms and finds that she is 60 kilograms. Her bathroom scale
says 140 pounds. Write the equation expressing pounds in terms of kilograms. How much would she
weigh if she was 25 kilograms?
