Algebra I Polynomial Review Sheet
I. Determining Degree
State the degree of each polynomial.
1. 3x2y + 2xyz3 – 5x3 + y4
2. abc + 6a2b – 4ab2 – 10
3. 8
4. 8xyz5 – 7x2y4z + xyz – 4x
II. Adding/Subtracting Polynomials
5. (5x2y + 6xy – 3xy2) + (2xy – 10x2y + 2xy2)
6. (7m3 + 5m2 – 8m + 3) – (10m3 + 3m2 – 8m – 3)
7. Add 3x2 + 5x + 2 to 8x2 – 6.
8. What is the result when p2 – 4p + 1 is subtracted from 3p2 + p – 5?
III. Properties of Powers
Simplify.
9.
( 3x 4 ) 2
x3
10. (5x2y)(–3x3y–4)
3 
11.  x 3 
4 
2
12.
16 x 3 yz 5
4 xy 2 z
IV. Multiplying Polynomials
13. x2(3x + 5)
14. 3xy2(4xy3 + xy + 2)
15. (x + 6)(2x – 3)
16. (3m + 1)(4m + 5)
17. (2x – 7)2
18. (4a + 9)(4a – 9)
VI. Applications
19. What is the area of a square whose perimeter is 16x + 28?
20. Bradley is extending his rectangular living room. The original dimensions are 6 feet by 11 feet. If he
extended his room by x + 8 feet, what is the new area? How many square feet of area did he add?
21. What is the area of the shaded region below? (Area of rectangle = Lw
x+6
Area of triangle = ½ bh)
x+2
2x + 4
3x – 4
22. What is the volume of a rectangular prism with a length of 8, a width of 3x + 7, and a height of 2x – 5?
(V = Lwh)