8 Mid-Chapter Quiz

Do you know HOW?

Find the degree of each monomial.

1. − 5 a 8 negative 5 , eh to the eighth
2. 4 x 2 y 3 4 , x squared , y cubed

Write each polynomial in standard form. Then name each polynomial based on its degree and number of terms.

3. 4 x + 3 x 2 4 x plus 3 , x squared
4. 7 p 2 − 3 p + 2 p 3 7 , p squared , minus 3 p plus 2 , p cubed

Simplify each sum or difference.

5. ( x 2 + 6 x + 11 ) + ( 3 x 2 + 7 x + 4 ) open , x squared , plus 6 x plus 11 close plus open 3 , x squared , plus 7 x plus 4 close
6. ( 5 w 3 + 3 w 2 + 8 w + 2 ) + ( 7 w 2 + 3 w + 1 ) open 5 , w cubed , plus 3 , w squared , plus 8 w plus 2 close plus open 7 , w squared , plus 3 w plus 1 close
7. ( 4 q 2 + 10 q + 7 ) − ( 2 q 2 + 7 q + 5 ) open 4 , q squared , plus 10 q plus 7 close minus open 2 , q squared , plus 7 q plus 5 close
8. ( 9 t 4 + 5 t + 8 ) − ( 3 t 2 − 6 t − 4 ) open 9 , t to the fourth , plus 5 t plus 8 close minus open 3 , t squared , minus 6 t minus 4 close

Simplify each product.

9. 6 x 2 ( 4 x 2 + 3 ) 6 , x squared , open 4 , x squared , plus 3 close
10. − 8 c 3 ( 3 c 2 + 2 c − 9 ) negative 8 , c cubed , open 3 , c squared , plus 2 c minus 9 close

Factor each polynomial.

11. 16 b 4 + 8 b 2 + 20 b 16 , b to the fourth , plus 8 , b squared , plus 20 b
12. 77 x 3 + 22 x 2 − 33 x − 88 77 , x cubed , plus 22 , x squared , minus 33 x minus 88

Simplify each product.

13. ( x + 2 ) ( x + 9 ) open x plus 2 close open x plus 9 close
14. ( 4 b − 1 ) ( b − 8 ) open 4 b minus 1 close open b minus 8 close
15. ( h + 2 ) ( 3 h 2 + h − 7 ) open h plus 2 close open 3 , h squared , plus h minus 7 close
16. ( z − 1 ) ( z 2 − 4 z + 9 ) open z minus 1 close open , z squared , minus 4 z plus 9 close
17. Design You are designing a rectangular rubber stamp. The length of the stamp is 2r + 3. The width of the stamp is r − 4 . r minus 4 .  What polynomial in standard form represents the area of the stamp?

Simplify each product.

18. ( r + 3 ) 2 open r plus 3 close squared
19. ( k − 3 ) ( k + 3 ) open k minus 3 close open k plus 3 close
20. ( 3 d + 10 ) 2 open 3 d plus 10 close squared
21. ( g + 10 ) ( g − 10 ) open g plus 10 close open g minus 10 close
22. ( 2 m − 7 ) 2 open 2 m minus 7 close squared
23. ( 7 h − 2 ) ( 7 h + 2 ) open 7 h minus 2 close open 7 h plus 2 close
24. Woodworking A birdhouse has a square base with side length 3 x − 4 . 3 x minus 4 .  What polynomial in standard form represents the area of the base?

Do you UNDERSTAND?

25. Writing Can the degree of a monomial ever be negative? Explain.

26. Geometry The figures below are rectangles. What polynomial in standard form represents the area of the shaded region?

    

27. Open-Ended Write a trinomial that has 9 x 2 9 , x squared  as the GCF of its term.
28. Open-Ended Write a trinomial of degree 4 such that the GCF of its terms is 1.
29. Reasoning Suppose n represents an even number. Write a simplified expression that represents the product of the next two even numbers.
30. Writing Describe how to simplify ( 8 k 2 + k − 1 ) − ( k 3 − 4 k 2 − 7 k + 15 ) . open 8 , k squared , plus k minus 1 close minus open , k cubed , minus 4 , k squared , minus 7 k plus 15 close .  Write your answer as a polynomial in standard form.

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