Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
Which of the following is a polynomial function?
|
|
|
2.
|
Which graph represents an odd-degree polynomial function with two
x-intercepts?
|
|
|
3.
|
How many x-intercepts are possible for the polynomial function  ?
|
|
|
4.
|
What is the restriction on x if  is divided by  ?
|
|
|
5.
|
Which set of values for x should be tested to determine the possible
zeros of  ? A | ±5, ±7, and ±35 | C | 1, 5, 7, 12, and
35 | B | ±1, ±5, ±7, and ±35 | D | 1, 5, 7, and 35 |
|
|
|
6.
|
Determine the value of k so that  is a factor of  . A | k = –1 | C | k = 14 | B | k = –14 | D | k = 1 |
|
|
|
7.
|
The fully factored form of  is
|
|
|
8.
|
One root of the equation  is
|
|
|
9.
|
Based on the graph of  , what are the real roots of  ?  A | –6, –2, 2, 4 | C | there are no real
roots | B | 6, 2, –2, –4 | D | impossible to determine |
|
|
|
10.
|
The graph that corresponds to the function  is
|
Short Answer
|
|
|
1.
|
a) Use long division to divide x3 +
3x2 – 7 by x + 2. Express the result in quotient form.
b)
Identify any restrictions on the variable.
c) Write the corresponding statement that can be
used to check the division.
d) Verify your answer.
|
|
|
2.
|
Factor fully.
a) x3 + 6x2 +
11x + 6
b) 4x3 – 11x2 –
3x
c) x4 – 81
|
|
|
3.
|
Solve.
a) 3x3 + 2x2 –
8x + 3 = 0
b) 2x3 + x2 – 10x
– 5 = 0
c) 5x4 = 7x2 – 2
|
Problem
|
|
|
1.
|
a) If x + 1 is a factor of ax4 +
bx2 + c, what is the value of a + b + c?
b)
Decide if x + 1 is a factor of each polynomial. Explain your
reasoning.
i) 3x4 + 3x2
– 6
ii) 17x4 –
10x2 – 7
iii)
x4 + x2 + 1
|
|
|
2.
|
Show that x + a is a factor of the polynomial P(x) =
(x + a)4 + (x + c)4 – (a –
c)4.
|
|
|
3.
|
Amit has designed a rectangular storage unit to hold large factory equipment.
His model has dimensions 1 m by 2 m by 4 m. By what amount should he increase each dimension to
produce an actual storage unit that is 9 times the volume of his model?
|