Polynomials Worksheet
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1
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5Topic 8
Review
TOPIC VOCABULARY
p. 369
p. 350
p. 375
p. 369
p. 363
p. 340
p. 340
p. 350
p. 350
p. 340
p. 350
p. 340
p. 370
p. 340
p. 357
p. 357
p. 340
p. 363
p. 340
p. 369
p. 340
p. 350
p. 350
Check Your Understanding
Match each vocabulary term with the description that best fits it.
A. determines P (a) by dividing the polynomial by x - a
1. Conjugate Root Theorem
2. Fundamental Theorem of Algebra
B. the degree equals the number of roots
3. Rational Root Theorem
C. minimizes guessing fraction and integer solutions
4. Remainder Theorem
D. complex numbers as roots come in pairs
8-1 Attributes of Polynomial Functions
Quick Review
Exercises
The standard form of a polynomial function is
Write each polynomial function in standard form, classify
n
n-1
+ c + a
P (x) = a
x
+ a
x
x + a
, where n is a
it by degree, and determine the end behavior of its graph.
n
n-1
1
0
nonnegative integer and the coefficients are real numbers.
5. y = 12 - x
4
6. y = 2x
2
+ 8 - 4x + x
3
A polynomial function is classified by degree. Its degree is
7. y = x
2
+ 7 - x
8. y = 10 - 3x
3
+ 3x
2
+ x
4
the highest degree among its monomial term(s). The degree
determines the possible number of turning points in the
9. If the volume of a cube can be represented by a
graph and the end behavior of the graph.
polynomial of degree 9, what is the degree of the
polynomial that represents each side length?
Example
10. A polynomial function P(x) has degree n. If n is even, is
Classify P(x) = -4x
2
+ x
4
by degree. How many possible
the number of turning points of the graph of P(x) even
turning points are there given the degree of P(x)?
or odd? What can you say about the number of turning
The degree of P(x) is 4, so its graph has either 1 or 3
points if n is odd?
turning points.
379
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