Unit 6 Practice Test
Find the degree of each monomial.
1.6xy
2.
–3b2c4
3. 12m7n
Simplify each sum or difference.
4. 6r3 + 7r3
5. 23u2v – 19u2v
6. (5g – 2g) + (2g2 + 6g)
7. The perimeter of a pentagon is 20t + 7. Four sides have the following lengths:
6t, 2t, 4t – 5, and 5t + 1. What is the length of the fifth side?
Simplify each product.
8. 3x(x + 6)
9. –z2(z – 9)
10. 2x(4x2 – 7x + 6)
12. 24n3 – 40n2 + 72n
13. 14b2c3 + 21bc5
Factor each polynomial.
11. 12x – 9
14. An artist is making a square stained glass window in which a green
glass circle is surrounded by blue glass. The side length of the
window is shown, and the area of the green piece is 64πx2. What is
the area of the blue glass? Write your answer in factored form.
Simplify each product.
15. (x – 2)(3x – 4)
16. (3x + 2)(x + 7)
17. (4x – 1)(2x + 5)
Simplify each product.
19. (x + 6)2
Complete.
22. k2 + 9k + 18 = (k + 3)(k +
21. (3x – 8)2
20. (2s + 7)2
)
23.
x2 – 11x + 28 = (x – 4)(x –
)
Simplify each product.
24. (v + 7)(v – 7)
25. (5s – t)2
26. (3p2 + 10q)(3p2 – 10q)
Find an expression for the area of each shaded region.
27.
28.
29. The area of a rectangular coffee table is given by the trinomial t2 + 7t – 8.
The table’s length is t + 8. What is the table’s width?
Factor each expression.
30. r2 + 12r + 27
31. g2 – 8g – 48
32. m2 + 2m – 35
33. 3d2 – 13d + 12
34. 8y2 + 60y + 72
35. 9w2 – 75w – 54
37. 2p4 + 6p3 – 8p2 – 4p
38. 8h2 + 36h + 16
Factor completely.
36. 6n3 – 24n2 + n – 4