Algebra I Polynomial Review Sheet



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. 10. (5x2y)(–3x3y–4) 11. 12.

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 Area of triangle = ½ bh)

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)

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x + 2

2x + 4

3x – 4

x + 6

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