Acc. Alg. II
W.S. 7.1 (day 2)
Name _______________________________
Assign. # _____
Determine whether each expression is a polynomial. If so, classify the polynomial by
degree and number of terms.
Polynomial Expression
1.
x2 x
 2
4 2
2.
3+
3.
4 x  3x  2
4.
4 x
 2
x2 2
5.
1 4
x  3x 2  2
4
6.
2x2 – 3x + 4 - 2x2
Yes/No
Classify by Degree and # of Terms
x3 x 2

2
7
Evaluate each polynomial expression for the indicated value of x. Show substitutions and
all steps. Keep answers exact.
-4 3 10 2
7
1
x x +
x7.
-x3 - x2 + x – 3 for x = -2
8.
for x = -11
11
11
11
11
9.
1 4 3 3
5
1
x  x  x  for x =
2
2
2
2
10.
The sum of 7x3 – 5x2 – ax – 7 and 5x3 – bx2 + cx + 5 is dx3 + ax2 + 4x – a. Find a,
b, c, and d. Show all work.
Acc. Alg. II – W.S. 7.1 day 2
11.
Page 2
The expression ax3 + 2x2 + cx + 1 is 5x3 – 3 greater than 3x3 + bx2 + d – 7x. Find a, b, c,
and d. Show work.
For ex. 12 – 13, write each sum or difference as a polynomial in standard form. Show work
1  1 3
3
2
1 3 1 2 1
2
12.
 x  x  x  x  x  x 
2
2
3  2
2
9
4
13.
Subtract (3x3 + 6x4 – 2x2 – 7) from (5x – 2x2 – 4x4)
Use your calculator to sketch the graph of each function. Use an appropriate viewing window. Be
sure to label intervals. Describe the general shape of the graph and state the range of the graph.
14.
b(x) = -x4 – 4x3 + 6x2 – x – 8
Description:
Domain:
Range:
Acc. Alg. II – W.S. 7.1 day 2
15.
Page 3
f(x) = -8x5 + 25x3 – 9x2 – 27
Description:
Domain:
Range:
16.
g(x) = 6x6 – 20x5 – 28x3 + 15x2 – 75x – 215
Description:
Domain:
Range:
Acc. Alg. II – W.S. 7.1 day 2
Page 4
Use your calculator to answer questions 17-18. Show steps.
17.
18.
19.
The cost of manufacturing a certain product is represented by the function
C(x) = 0.02x3 – 0.01x + 100 where x is the quantity of product. Show work.
A.
Is the function a polynomial? If so, classify the polynomial.
B.
What is the cost of manufacturing 15 items?
The profit from selling a certain product is represented by the function
M(p) = -0.002p3 + 0.05p2 – 0.01p, where p is the selling price. Show work.
A.
What profit will be earned if the selling price is $10?
B.
What is the maximum profit?
C.
For what selling price will the profit be the largest?
D.
What selling price will result in $0 profit?
Polynomials are used in business to express the cost of manufacturing products.
If the cubic function C(x) = x3 – 15x + 15 gives the cost of manufacturing x units
(in thousands) of a product, what is the cost to manufacture 10,000 units of the
product? Show work.
Ch. 5 Review:
20.
Solve for x.
6x2 – 8x + 3 = 0
Acc. Alg. II – W.S. 7.1 day 2
Page 5
x4 – 14x2 + 48 = 0
21.
Solve for x.
22.
Solve for x by completing the square. 2x2 + 5x = 3
23.
Write the quadratic function g(x) = 2x2 + 12x + 13 in vertex form and give the
coordinates of the vertex.
Ch. 2 Review
Simplify the following. Write all answers with positive exponents.
-1 2 x3
2 a
24.
x 2
3a
25.

2 x
xy
3 1

3
2 4
3 x y
2 2
( xy )
Acc. Alg. II – W.S. 7.1 day 2
Some Answers – Remember, I don’t guarantee my answers. Ask Questions!!!!
1.
3.
5.
8.
10.
12.
14.
15.
17B.
18A.
18C.
19.
20.
21.
22.
23.
24.
25.
yes; quadratic trinomial
no
yes; quartic trinomial
4036
11
a = 2, b = -7, c = 6, d = 12
-¼ x3 + ½ x2 – 2x + 1/9
M-shape, 2 peaks, 1 valley; r:(-, 93.4]
S-shape; 2 peaks, 2 valleys; R:(-, )
$167.35
$2.90
$16.57
$865
4 2 i
x
6
x   6 or x  2 2
x = -3, ½
V(-3, -5)
a x 5
6
9 x 2 y8
2
Page 6