8 Chapter Test

Do you know HOW?

Write each polynomial in standard form.

1. 2 x − 3 x 2 + 6 + 5 x 3 2 x minus , 3 x squared , plus 6 plus , 5 x cubed
2. 7 + 9 x + 2 x 2 + 8 x 5 7 plus 9 x plus , 2 x squared , plus , 8 x to the fifth

Simplify. Write each answer in standard form.

3. ( 4 x 2 + 9 x + 1 ) + ( 2 x 2 + 7 x + 13 ) open , 4 x squared , plus 9 x plus 1 close plus open , 2 x squared , plus 7 x plus 13 close
4. ( 8 x 2 + 5 x + 7 ) − ( 5 x 2 + 8 x − 6 ) open , 8 x squared , plus 5 x plus 7 close minus open , 5 x squared , plus 8 x minus 6 close
5. ( 5 x 4 + 7 x + 2 ) − ( 3 x 2 − 2 x + 9 ) open , 5 x to the fourth , plus 7 x plus 2 close minus open , 3 x squared , minus 2 x plus 9 close
6. ( − 7 x 3 + 4 x − 6 ) + ( 6 x 3 + 10 x 2 + 3 ) open negative , 7 x cubed , plus 4 x minus 6 close plus open , 6 x cubed , plus , 10 x squared , plus 3 close

Simplify each product. Write in standard form.

7. − p ( 8 p 2 + 3 p ) negative p open , 8 p squared , plus 3 p close
8. ( r + 8 ) ( r + 6 ) open r plus 8 close open r plus 6 close
9. ( 5 w − 6 ) ( 2 w + 7 ) open 5 w minus 6 close open 2 w plus 7 close
10. ( 4 s + 5 ) ( 7 s 2 − 4 s + 3 ) open 4 s plus 5 close open , 7 s squared , minus 4 s plus 3 close
11. ( q − 1 ) 2 open q minus 1 close squared
12. ( 3 g − 5 ) ( 3 g + 5 ) open 3 g minus 5 close open 3 g plus 5 close
13. Camping A rectangular campground has length 4x + 7 and width 3 x − 2 . 3 x minus 2 .  What is the area of the campground?

Find the GCF of the terms of each polynomial.

14. 16 x 6 + 22 x 2 + 30 x 5 16 x to the sixth , plus , 22 x squared , plus , 30 x to the fifth
15. 7 v 3 − 10 v 2 + 9 v 4 7 v cubed , minus , 10 v squared , plus , 9 v to the fourth

Factor each expression.

16. x 2 + 17 x + 72 x squared , plus 17 x plus 72
17. 4 v 2 − 16 v + 7 4 v squared , minus 16 v plus 7
18. n 2 − 16 n + 64 n squared , minus 16 n plus 64
19. 6 t 2 − 54 6 t squared , minus 54
20. y 2 − 121 y squared , minus 121

Factor completely.

21. 7 h 4 − 4 h 3 + 28 h 2 − 16 h 7 h to the fourth , minus , 4 h cubed , plus , 28 h squared , minus 16 h
22. 15 t 3 + 2 t 2 − 45 t − 6 15 t cubed , plus , 2 t squared , minus 45 t minus 6
23. 6 n 4 + 15 n 3 − 9 n 2 6 n to the fourth , plus , 15 n cubed , minus , 9 n squared
24. 9 v 4 + 12 v 3 − 18 v 2 − 24 v 9 v to the fourth , plus , 12 v cubed , minus , 18 v squared , minus 24 v
25. Art The area of a square painting is 81 p 2 + 90 p + 25 . 81 p squared , plus 90 p plus 25 .  What is the side length of the painting?

Do you UNDERSTAND?

26. Open-Ended Write a trinomial with degree 5.
27. Writing Explain how to use the Distributive Property to multiply two binomials. Include an example.

28. Geometry What is an expression for the area of the figure? Write your answer as a polynomial in standard form.

    

29. Open-Ended What are three different values that complete the expression x 2 +   x + 24 x squared , plus begin box , , end box x plus 24  so that you can factor it into the product of two binomials? Show each factorization.

Write the missing value in each perfect-square trinomial.

30. n 2 +   n + 81 n squared , plus begin box , , end box n plus 81
31. 16 y 2 − 56 y +   16 y squared , minus 56 y plus begin box , , end box
32.   p 2 + 30 p + 25 begin box , , end box , p squared , plus 30 p plus 25

33. Reasoning The expression ( x − 2 ) 2 − 9 open x minus 2 close squared . minus 9  has the form a 2 − b 2 . eh squared , minus , b squared , .

    1. Identify a and b.
    2. Factor ( x − 2 ) 2 − 9 . open x minus 2 close squared . minus 9 .  Then simplify.

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