Adding & Subtracting Polynomials
Name:
A.10.A add and subtract polynomials of degree one and degree two
Find each sum or difference.
1. (4y + 5) + (–7y – 1)
2. (–x 2 + 3x) – (5x + 2x 2 )
3. (4k 2 + 8k + 2) – (2k + 3)
4. (2m2 + 6m) + (m2 – 5m + 7)
5. (5a2 + 6a + 2) – (7a2 – 7a + 5)
6. (–4p2 – p + 9) + (p2 + 3p – 1)
7. (x 3 – 3x + 1) – (x 3 + 7 – 12x)
8. (6x 2 – x + 1) – (–4 + 2x 2 + 8x)
9. (4y 2 + 2y – 8) – (7y 2 + 4 – y)
10. (w 2 – 4w – 1) + (–5 + 5w 2 – 3w)
11. (2x3 + 2x2 - 3x + 1) – (x3 - 2x2 + x – 4)
12. The measures of two sides of a triangle are given. If P is the perimeter, and P = 10x + 5y, find the
measure of the third side.
13. Two polynomials model different financial information for a company. The first polynomial
40,000 + 3x2 represents the gross monthly income from selling x units, while the second one,
0.05x + 100 represents the monthly production cost of x units. Which of the following expressions models
gross income less production costs?
a. 40000 + 3x2 – 0.05x + 100
b. (40000 – 100) + 3x2 – 0.05x
c. 3x2 – 0.05x + 39900
d. 3x2 – 0.05x + 40100
e. a and b
f. b and c
14. The polynomial s 3 – 70s 2 + 1500s – 10,800 models the income (revenue) a company makes on
selling an item at a price s. The polynomial s 3 – 30s 2 + 450s – 5000 models the cost a company pays for
selling an item at a price s. Write a polynomial that expresses the profit from the sale of the item. In
business the profit equation is represented by p = r – c, where p is profit, r is revenue, and c is cost.
15. A company delivers their product in cubic boxes that have volume x 3. When the company begins to
manufacture a second product, manufacturing designs a new shipping box that is 3 inches longer in one
dimension and 1 inch shorter in another dimension. The volume of the new box is x3 + 2x2 - 3x. What is
the total volume of 4 of each kind of box? Find an expression that shows the difference in volume
between the two boxes.
16. Jen, a biologist, is growing bacterial cultures at different temperatures as part of her research. The
number of cells in the culture growing at 25°C is given by the polynomial t2 + 4t + 4, where t is the time
elapsed in minutes. The number of cells in the second culture growing at 35°C is modeled by the
polynomial t2 + 4. She needs to measure the success of the 25°C culture over the 35°C culture. Find the
polynomial representing how many more cells are in the 25°C culture for time t. How many more cells
are there after 15 minutes?
17. Jane and Jill were simplifying the expression (2x2 + x) + 2(-x2 + x) and obtained different answers.
Who is correct and why?
Jane
(2x2 + x) + 2(-x2 + x)
(2x2 + x) + (-x2 + x) + (-x2 + x)
(2x2 - x2 - x2 ) + (x + x + x)
3x
Jill
(2x2 + x) + 2(-x2 + x)
(2x2 + x) - 2x 2 + x
2x2 - 2x 2 + x + x
2x