Academic Worksheet 12.1
Tell whether the expression is a polynomial. If it is a polynomial, list its terms and classify it.
1.
9𝑥
2
4.
7𝑛 −1
+ 6
+ 4𝑛 −2
2.
– 𝑚
5.
𝑎 + 8𝑎𝑏 2 − 5
3.
2𝑝 − 𝑝
6.
3𝑦 2
2
+ 1
+ 4𝑦 −2 − 10
Find the degree of the polynomial.
7.
3𝑐 4
10.
𝑡
3
− 5𝑐
− 𝑠
4
2 − 4 8.
2 + 𝑝 2 − 8𝑝
11.
9𝑚𝑛 + 𝑚𝑛
2
9.
– 𝑤
4
+ 𝑤
3
12.
5𝑥𝑦 + 10𝑥
− 6
2 𝑦
2
Write the expression as a polynomial in standard form.
13.
5ℎ 2 + 6 − ℎ 2 − 1 + 2ℎ
15.
11𝑦 + 5(3 − 2𝑦
2 ) + 6
14.
4𝑧 − 2𝑧
16.
𝑎
2
2 + 9𝑧 − 11
− 7 − 2(4𝑎 + 8)
Evaluate the polynomial when 𝑥 = 5 .
17.
6 − 3𝑥 18.
𝑥
2
+ 𝑥 − 8 19.
9𝑥 − 𝑥
2
+ 2𝑥
3
+ 14
Write a polynomial expression for the perimeter of the figure. Give your answer in standard form.
20.
21.
22.
The height (in feet) of a golf ball 𝑡 seconds after it is hit is given by the polynomial −16𝑡
2
150𝑡 .
+ a.
What is the degree of the polynomial? b.
What is the height of the golf ball 2 seconds after it is hit? c.
What is the height of the golf ball 4 seconds after it is hit?
Evaluate the polynomial when 𝑥 = −2 and 𝑦 = 1 .
23.
7𝑥𝑦 + 3𝑦 24.
𝑦
2
− 3𝑥𝑦 + 𝑥
2

Academic Worksheet 12.2
Find the sum.
1.
(3𝑎 2
+ 2) + (𝑎
2
− 10)
3.
(2𝑑 + 4) + (3𝑑 2 − 9𝑑 − 16)
Find the perimeter of the triangle.
5.
2.
(4𝑦 2
+ 𝑦 − 9) + (𝑦
2
− 2)
4.
(−𝑛 2 − 2𝑛 + 4) + (𝑛 2 + 7𝑛 − 5)
6.
7.
The polynomials below approximate the number of students enrolled as business and science majors in a particular college for each year during the period 1990-2000. In each polynomial, 𝑥 represents the number of years since 1990.
Business majors: −17𝑥
2
+ 200𝑥 + 732
Science majors: 28𝑥 + 956
Write a polynomial that gives the total number of students enrolled each year as business and science majors.
Find the difference.
8.
(2𝑥 2
− 11) − (5𝑥
2
10.
(10𝑡 − 1) − (3𝑡 2
− 14)
− 4𝑡 + 6)
9.
(9𝑤 2
11.
(−𝑛 2
− 𝑤 − 13) − (2𝑤
2
− 6𝑛 − 15) − (𝑛 2
− 16)
+ 7𝑛 − 3)
12.
For a company that manufactures and sells model airplanes, the cost (in dollars) of producing 𝑥 model airplanes is represented by the polynomial 110 + 32𝑥 . The revenue (in dollars) for selling 𝑥 model airplanes is represented by the polynomial 85𝑥 − 𝑥 2
. The profit can be found by subtracting the cost from the revue. Write a polynomial expression for the profit.

Academic Worksheet 12.3
Find the product.
1.
−3𝑦(2𝑦
2
4.
9𝑧(8𝑧 2
− 6𝑦)
− 3𝑧 − 10)
2.
(7𝑐 3
− 9)4𝑐
5.
−6𝑤(−𝑤 2 + 3𝑤 + 1)
3.
11𝑝(4𝑝
2
− 3𝑝)
6.
(𝑡 2 − 6𝑡 − 12)4𝑡 2
Find the quotient.

12 x
2
7.
6 x
3
3 x
10.
5 y
6 

3 y y
2
5  y
3
8.
11.

14 z
2 
28 z

7 z
32 b
4 
24 b
3

8 b
2

16 b
2
9.

8 a
4 
20 a
3

4 a
2

16 a
2
12.

6 d
3 
22 d
2 
32 d
2 d
13.
You have 30 feet of wire fencing that you want to use to make a rectangular pen for chickens.
Let 𝑙 be the length of the pen. What is a polynomial expression in terms of 𝑙 for the area of the pen?
14.
The length of a trampoline is 3 feet less than twice the width. Let 𝑤 be the width of the trampoline. Write a polynomial expression in terms of 𝑤 for the area of the trampoline. Give your answer in standard form.

Academic Worksheet 12.4
Find the product.
1.
(𝑥 + 4)(𝑥 + 2)
4.
(−4𝑝 + 9)(−3𝑝 + 1)
Complete the table.
7.
2.
(2𝑐 − 4)(4𝑐 − 7)
5.
(3𝑤 − 7)(−9𝑤 − 4)
8.
3.
(7𝑦 + 1)(2𝑦 + 8)
6.
(5𝑚 − 2) 2
9.
Write a polynomial expression for the area of the figure. Give your answer in standard form.
10.
11.
12.
You are enlarging a photo that is 4 inches long and 3 inches wide. The length and width of the enlargement are 𝑥 times the length and width of the original photo. The enlargement will have a 1.5-inch mat. Write a polynomial expression for the combined area of the enlargement and mat.
13.
The figure shown is composed of a triangle and a rectangle. Write a polynomial expression for the area of the figure. Give your answer in standard form.