Pre-Calc 120B
Nov 10, 2021
Decoding Polynomials
Instructions: The questions on the following page refer to the polynomial functions
below. Answer the questions, and use the cypher key to decypher the riddle.
a(x)
b(x)
c(x)
d(y)
e(x)
f(y)
g(x)
h(x)
i(x)
𝑎 𝑥 = 9
𝑏 𝑥 = 𝑥 ! + 2𝑥 + 11
𝑐 𝑥 = 𝑥! + 6
𝑑 𝑦 = 3𝑦 + 10
𝑒 𝑥 = 7𝑥 ! + 3𝑥 ! + 𝑥 ! + 2𝑥 + 8
𝑓 𝑦 = (𝑦 + 3)(𝑦 − 1)(𝑦 − 2)(𝑦 + 5)
𝑔 𝑥 = 11𝑥 ! + 𝑥 ! − 𝑥 ! + 3𝑥 + 7
ℎ 𝑥 = 𝑥 ! + 5𝑥 ! + 1
j(x)
k(x)
m(x)
Cypher Key:
Answer
Decoded
0
O
1
I
2
A
3
E
4
L
5
D
6
M
7
H
8
G
9
R
10 11 +
S T P
N
X Y
W Y
Useful Terminology:
Term: A variable and its coefficient, including constant terms. E.g. 3𝑥 ! or 10
Variable: A quantity that can change, usually represented by a letter. E.g. x or y
Constant: A term in which a variable does not occur. E.g. 6
Coefficient: The number in front of a variable. E.g. The term 3𝑥 ! has a coefficient of 3.
Degree (of the polynomial function): This is the highest exponent of the variable when the
function is in standard form. E.g. 𝑔 𝑥 = 11𝑥 ! + 𝑥 ! − 𝑥 ! + 3𝑥 + 7 has a degree of 4.
The Leading Coefficient: The coefficient of the term with the highest exponent, which
should be the first term in standard form.
Roots/zeros occur when the function passes through the x-axis (x = 0).
Pre-Calc 120B
Nov 10, 2021
Clue:
Answer
Decoded
The variable in a(x)
X
W
The constant term in g(x)
The variable in d(y)
The degree of e(x)
The degree of d(y)
The number of terms in g(x)
The constant in b(x)
The leading coefficient of e(x)
The number of terms in b(x)
The sign of the leading coefficient of i(x)
The number of roots of i(x)
The degree of j(x)
The variable in f(y)
The sign of the leading coefficient in m(x)
The degree of a(x)
The constant in c(x)
The number of terms of a(x)
The degree of c(x)
The degree of f(y)
The sign of the leading coefficient in k(x)
The number of roots of f(y)
The degree of i(x)
The sign of the leading coefficient of j(x)
The leading coefficient in g(x)
The degree of k(x)
The number of roots of k(x)
The degree of m(x)
?