Name _________________________________
Ch. 5 Study Guide
Date ___________________
Hour________
7. A rectangle has a length of
and a width of
.
Which equation below describes the perimeter, P,
of the rectangle in terms of x?
Simplify the expression.
1.
Factor the polynomial completely.
____
8.
2.
Find the real-number solutions of the equation.
Complete the statement to describe the end
behavior of the graph of the function.
____
9.
3.
Decide whether the function is a polynomial
function. If so, state its degree, type, and leading
coefficient.
Divide.
4.
10.
Find the sum or difference.
5.
____
Find the product.
6.
11.
_
_
Divide using polynomial long division.
12.
Write a polynomial function f of least degree that
has rational coefficients, a leading coefficient of
1, and the given zeros.
16.
17.
Determine the possible numbers of positive
real zeros, negative real zeros, and imaginary zeros
for
.
Given polynomial function f and a zero of f, find
the other zeros.
13.
BONUS
Explain why a polynomial of odd degree must have
at least one real zero.
List the possible rational zeros of the function
using the rational zeros theorem.
14.
Suppose a polynomial function f has at least 2 real
zeros and at least 1 imaginary zero. The graph of
the function crosses the x-axis 5 times. What is the
minimum degree f can have? Justify your answer.
Find all zeros of the polynomial function.
15.
Ch. 5 Test
Answer Section
1. ANS:
PTS: 1
DIF:
Level B
2. ANS:
PTS: 1
DIF:
Level B
3. ANS:
4. ANS: yes; degree 2; quadratic; leading coefficient 4
PTS: 1
PTS: 1
DIF:
DIF:
Level B
Level A
5. ANS:
PTS: 1
DIF:
Level B
6. ANS:
7. ANS:
PTS: 1
PTS: 1
DIF:
DIF:
Level A
Level B
8. ANS:
9. ANS: 0, 4
PTS: 1
PTS: 1
DIF:
DIF:
Level A
Level A
10. ANS:
PTS: 1
DIF:
Level A
11. ANS:
PTS: 1
DIF:
Level B
12. ANS:
PTS: 1
DIF:
Level A
13. ANS: 3, -3
14. ANS:
15. ANS:
PTS: 1
PTS: 1
PTS: 1
DIF:
DIF:
DIF:
Level B
Level A
Level B
16. ANS:
17. ANS:
PTS: 1
PTS: 1
DIF:
DIF:
Level B
Level B
18. ANS:
PTS: 1
DIF: Level B
Sample answer: The number of zeros of a function is equal to the degree of the polynomial function. Because
complex zeros occur in conjugate pairs, only an even number of imaginary zeros can occur. Therefore, if a
polynomial of odd degree has imaginary zeros, it must also have at least one zero that is a real number.
19. ANS:
PTS: 1
DIF: Level B
Sample answer: If the graph of the polynomial crosses the x-axis 5 times, the polynomial has at least 5 real
zeros. If it has one imaginary zero, there must be at least one other imaginary zero, because imaginary zeros
come in pairs. Therefore, the minimum degree of f is 5 + 2 = 7