State the degree and leading coefficient of each
polynomial in one variable. If it is not a
polynomial in one variable, explain why.
1.11x6– 5x5 + 4x2
ANSWER:
degree = 6, leading coefficient = 11
2.–10x7 – 5x3 + 4x – 22
ANSWER:
degree = 7, leading coefficient = –10
3.14x4 – 9x3 + 3x –4y
ANSWER:
not in one variable because there are two variables, x
and y
4.8x5 –3x2 + 4xy – 5
ANSWER:
not in one variable because there are two variables, x
and y
Find w(5) and w(–4) for each function.
5.w(x) = –2x3 + 3x – 12
ANSWER:
w(5) = –247; w(–4) = 104
6.w(x) = 2x4 – 5x3 + 3x2 – 2x + 8
ANSWER:
w(5) = 698; w(–4) = 896
If c(x) = 4x3 – 5x2 + 2 and d(x) = 3x2 + 6x –10,
find each value.
7.c(y3)
ANSWER:
4y9 – 5y 6 + 2
For each graph,
a. describe the end behavior,
b. determine whether it represents an odd-
degree or an even-degree function, and
c. state the number of real zeros.
11.
ANSWER:
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at three points, so
there are three real zeros.
12.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at zero points, so
there are no real zeros.
For each graph,
a. describe the end behavior,
b. determine whether it represents an odd-
degree or an even-degree function, and
c. state the number of real zeros.
35.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at four points, so
there are four real zeros.
36.
ANSWER:
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, so
there is one real zero.
37.
ANSWER:
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, so
there is one real zero.
38.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at no points, so
there are no real zeros.
39.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at two points, so
there are two real zeros.
40.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at two points, so
there are two real zeros.
Use the degree and end behavior to match each
polynomial to its graph.
A.
B.
C.
D.
47.
f(x) = x3 + 3x2 – 4x
ANSWER:
D
48.
f(x) = – 2x2 + 8x + 5
ANSWER:
B
49.
f(x) = x4 – 3x2 + 6x
ANSWER:
A
50.
f(x) = – 4x3 – 4x2 + 8
ANSWER:
C
69.SHORT RESPONSE Four students solved the
same math problem. Each student’s work is shown
below. Who is correct?
Student A
Student B
Student C
Student D
ANSWER:
Student A
Solve each inequality.
80.
ANSWER:
State the degree and leading coefficient of each
polynomial in one variable. If it is not a
polynomial in one variable, explain why.
1.11x6– 5x5 + 4x2
ANSWER:
degree = 6, leading coefficient = 11
2.–10x7 – 5x3 + 4x – 22
ANSWER:
degree = 7, leading coefficient = –10
3.14x4 – 9x3 + 3x –4y
ANSWER:
not in one variable because there are two variables, x
and y
4.8x5 –3x2 + 4xy – 5
ANSWER:
not in one variable because there are two variables, x
and y
Find w(5) and w(–4) for each function.
5.w(x) = –2x3 + 3x – 12
ANSWER:
w(5) = –247; w(–4) = 104
6.w(x) = 2x4 – 5x3 + 3x2 – 2x + 8
ANSWER:
w(5) = 698; w(–4) = 896
If c(x) = 4x3 – 5x2 + 2 and d(x) = 3x2 + 6x –10,
find each value.
7.c(y3)
ANSWER:
4y9 – 5y 6 + 2
For each graph,
a. describe the end behavior,
b. determine whether it represents an odd-
degree or an even-degree function, and
c. state the number of real zeros.
11.
ANSWER:
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at three points, so
there are three real zeros.
12.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at zero points, so
there are no real zeros.
For each graph,
a. describe the end behavior,
b. determine whether it represents an odd-
degree or an even-degree function, and
c. state the number of real zeros.
35.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at four points, so
there are four real zeros.
36.
ANSWER:
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, so
there is one real zero.
37.
ANSWER:
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, so
there is one real zero.
38.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at no points, so
there are no real zeros.
39.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at two points, so
there are two real zeros.
40.
ANSWER:
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at two points, so
there are two real zeros.
Use the degree and end behavior to match each
polynomial to its graph.
A.
B.
C.
D.
47.
f(x) = x3 + 3x2 – 4x
ANSWER:
D
48.
f(x) = – 2x2 + 8x + 5
ANSWER:
B
49.
f(x) = x4 – 3x2 + 6x
ANSWER:
A
50.
f(x) = – 4x3 – 4x2 + 8
ANSWER:
C
69.SHORT RESPONSE Four students solved the
same math problem. Each student’s work is shown
below. Who is correct?
Student A
Student B
Student C
Student D
ANSWER:
Student A
Solve each inequality.
80.
ANSWER:
eSolutionsManual-PoweredbyCogneroPage1
4-3 Polynomial Functions
