Mth 163 Test-Unit II Name___________________________
Sections 4.2-4.5, 2.5
1. Identify the left-hand and right-hand behavior of the graph of the polynomial
function f(x) = 6x
3
– 5x + 4.
2. Find a polynomial function that has zeros at -3, -1, and -2. Do not leave it in
factored form, but multiply out your answer.
3. Use the Intermediate Value Theorem to determine an interval bounded by integers
one unit in length in which the polynomial function is guaranteed to have a zero.
[EXPLAIN]
f(x) = 3x
5
– 9x
4
+ 5x
3
– 4x
2
+ x – 3
4. Use synthetic division to determine which of the following is a solution of the
equation 3x
4
– 2x
3
+ 26x
2
– 18x – 9 = 0.
[A] 3 [B] 1 [C] - 3 [D] 1/3 [E] None of these
5. Use synthetic division to divide 4x
4
– 4x
3
-8x – 14 by x – 2. Show your work and
state the quotient and remainder.
6. Factor 2x
3
+ 15x
2
+ 27x +10 given that x+2 is one of the factors. SHOW YOUR
WORK.
7. Determine the maximum number of zeros of the polynomial function
f(x) = 7x
2
+ 7x – 7x +2.
8. Use the Rational Zero Theorem to determine all possible rational zeros of
f(x) = 3x
5
– 6x
3
– 2x
2
+ 9
Do not find the actual zeros.
9. Find all the real zeros of the function f(x) = x
3
+ 2x
2
– 13x + 10. SHOW YOUR
WORK.
10. A polynomial function of degree 5 whose coefficients are real numbers has the
zeros 2, -9i, and -9+i. Identify the remaining zeros.
11. Write this polynomial in completely factored form: 10x
3
+29x
2
+ 4x – 15. SHOW
YOUR WORK.
12. Use the Remainder Theorem, not direct substitution, to find f(-2) when
f(x) = 4x
3
+ 3x + 10. Show your work and specify what f(-2) is.
13. Wouldn’t it be nice to win a million dollars? Most people think so, but one thing
many forget to consider is the amount of taxes that must be paid on the winnings. The
table below shows the relationship between the winnings and the approximate amount
of taxes to be paid to the IRS. Draw a scatter plot to model the data. Then find an
equation for the best-fit line and use the equation to estimate the amount of taxes to
be paid on winnings of $5,300,000.
Amount Won Taxes Due
$470,000 $100,000
$670,000 $180,000
$1,420,000 $480,000
$1,995,000 $710,000
2,545,000 $930,000
...
1. Mth 163 Test-Unit II
Name___________________________
Sections 4.2-4.5, 2.5
1. Identify the left-hand and right-hand behavior of the graph
of the polynomial
function f(x) = 6x
3
– 5x + 4.
2. Find a polynomial function that has zeros at -3, -1, and -2.
Do not leave it in
factored form, but multiply out your answer.
3. Use the Intermediate Value Theorem to determine an interval
bounded by integers
one unit in length in which the polynomial function is
guaranteed to have a zero.
[EXPLAIN]
f(x) = 3x
5
– 9x
2. 4
+ 5x
3
– 4x
2
+ x – 3
4. Use synthetic division to determine which of the following is
a solution of the
equation 3x
4
– 2x
3
+ 26x
2
– 18x – 9 = 0.
[A] 3 [B] 1 [C] - 3 [D] 1/3 [E] None of these
5. Use synthetic division to divide 4x
4
– 4x
3. 3
-8x – 14 by x – 2. Show your work and
state the quotient and remainder.
6. Factor 2x
3
+ 15x
2
+ 27x +10 given that x+2 is one of the factors. SHOW YOUR
WORK.
7. Determine the maximum number of zeros of the polynomial
function
f(x) = 7x
2
+ 7x – 7x +2.
8. Use the Rational Zero Theorem to determine all possible
rational zeros of
f(x) = 3x
5
4. – 6x
3
– 2x
2
+ 9
Do not find the actual zeros.
9. Find all the real zeros of the function f(x) = x
3
+ 2x
2
– 13x + 10. SHOW YOUR
WORK.
10. A polynomial function of degree 5 whose coefficients are
real numbers has the
zeros 2, -9i, and -9+i. Identify the remaining zeros.
5. 11. Write this polynomial in completely factored form: 10x
3
+29x
2
+ 4x – 15. SHOW
YOUR WORK.
12. Use the Remainder Theorem, not direct substitution, to find
f(-2) when
f(x) = 4x
3
+ 3x + 10. Show your work and specify what f(-2) is.
6. 13. Wouldn’t it be nice to win a million dollars? Most people
think so, but one thing
many forget to consider is the amount of taxes that must be paid
on the winnings. The
table below shows the relationship between the winnings and
the approximate amount
of taxes to be paid to the IRS. Draw a scatter plot to model the
data. Then find an
equation for the best-fit line and use the equation to estimate
the amount of taxes to
be paid on winnings of $5,300,000.
Amount Won Taxes Due
$470,000 $100,000
$670,000 $180,000
$1,420,000 $480,000
$1,995,000 $710,000
2,545,000 $930,000
![Mth 163 Test-Unit II
Name___________________________
Sections 4.2-4.5, 2.5
1. Identify the left-hand and right-hand behavior of the graph
of the polynomial
function f(x) = 6x
3
– 5x + 4.
2. Find a polynomial function that has zeros at -3, -1, and -2.
Do not leave it in
factored form, but multiply out your answer.
3. Use the Intermediate Value Theorem to determine an interval
bounded by integers
one unit in length in which the polynomial function is
guaranteed to have a zero.
[EXPLAIN]
f(x) = 3x
5
– 9x](https://image.slidesharecdn.com/mth163test-unitiina-221101071004-d83d247b/85/mth-163-testunit-ii-nadocx-1-320.jpg)
![4
+ 5x
3
– 4x
2
+ x – 3
4. Use synthetic division to determine which of the following is
a solution of the
equation 3x
4
– 2x
3
+ 26x
2
– 18x – 9 = 0.
[A] 3 [B] 1 [C] - 3 [D] 1/3 [E] None of these
5. Use synthetic division to divide 4x
4
– 4x](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)