Practice and Problem-Solving Exercises

A Practice

See Problems 1, 2, and 3.

Divide.

8. ( x 6 − x 5 + x 4 ) ÷ x 2 open , x to the sixth , minus , x to the fifth , plus , x to the fourth , close divides , x squared
9. ( 12 x 8 − 8 x 3 ) ÷ 4 x 4 open 12 , x to the eighth , minus 8 , x cubed , close divides 4 , x to the fourth
10. ( 9 c 4 + 6 c 3 − c 2 ) ÷ 3 c 2 open 9 , c to the fourth , plus 6 , c cubed , minus , c squared , close divides 3 , c squared
11. ( n 5 − 18 n 4 + 3 n 3 ) ÷ n 3 open , n to the fifth , minus 18 , n to the fourth , plus 3 , n cubed , close divides , n cubed
12. ( 8 q 2 − 32 q ) ÷ 2 q 2 open 8 , q squared , minus 32 q close divides 2 , q squared
13. ( 7 t 5 + 14 t 4 − 28 t 3 + 35 t 2 ) ÷ 7 t 2 open 7 , t to the fifth , plus 14 , t to the fourth , minus 28 , t cubed , plus 35 , t squared , close divides 7 , t squared
14. ( 6 x 4 − 5 x 3 + 6 x 2 ) ÷ 2 x 2 open 6 , x to the fourth , minus 5 , x cubed , plus 6 , x squared , close divides 2 , x squared
15. ( 21 t 5 + 3 t 4 − 11 t 3 ) ÷ 7 t 3 open 21 , t to the fifth , plus 3 , t to the fourth , minus 11 , t cubed , close divides 7 , t cubed
16. ( n 2 − 5 n + 4 ) ÷ ( n − 4 ) open , n squared , minus 5 n plus 4 close divides open n minus 4 close
17. ( y 2 − y + 2 ) ÷ ( y + 2 ) open , y squared , minus y plus 2 close divides open y plus 2 close
18. ( 3 x 2 − 10 x + 3 ) ÷ ( x − 3 ) open 3 , x squared , minus 10 x plus 3 close divides open x minus 3 close
19. ( − 4 q 2 − 22 q + 12 ) ÷ ( 2 q + 1 ) open negative 4 , q squared , minus 22 q plus 12 close divides open 2 q plus 1 close
20. ( 5 t 2 − 500 ) ÷ ( t + 10 ) open 5 , t squared , minus 500 close divides open t plus 10 close
21. ( 2 w 3 + 3 w − 15 ) ÷ ( w − 1 ) open 2 , w cubed , plus 3 w minus 15 close divides open w minus 1 close
22. ( 3 b 3 − 10 b 2 + 4 ) ÷ ( 3 b − 1 ) open 3 , b cubed , minus 10 , b squared , plus 4 close divides open 3 b minus 1 close
23. ( c 3 − c 2 − 1 ) ÷ ( c − 1 ) open , c cubed , minus , c squared , minus 1 close divides open c minus 1 close

Write an expression for the missing dimension in each figure.

See Problem 4.

Divide.

26. ( 49 + 16 b + 2 b 2 ) ÷ ( 2 b + 4 ) open 49 plus 16 b plus 2 , b squared , close divides open 2 b plus 4 close
27. ( 4 a 2 − 6 + 3 a ) ÷ ( 7 + 4 a ) open 4 , eh squared , minus 6 plus 3 eh close divides open 7 plus 4 eh close
28. ( 39 w + 14 + 3 w 2 ) ÷ ( 9 + 3 w ) open 39 w plus 14 plus 3 , w squared , close divides open 9 plus 3 w close
29. ( 4 t + 2 t 2 − 9 ) ÷ ( − 6 + 2 t ) open 4 t plus 2 , t squared , minus 9 close divides open negative 6 plus 2 t close
30. ( − 13 x + 6 x 3 − 6 − x 2 ) ÷ ( 3 x − 5 ) open negative 13 x plus 6 , x cubed , minus 6 minus , x squared , close divides open 3 x minus 5 close
31. ( 6 − q + 8 q 3 − 4 q 2 ) ÷ ( 2 q − 2 ) open 6 minus q plus 8 , q cubed , minus 4 , q squared , close divides open 2 q minus 2 close
32. ( 6 x 4 + 4 x 3 − x 2 ) ÷ ( 6 + 2 x ) open 6 , x to the fourth , plus 4 , x cubed , minus , x squared , close divides open 6 plus 2 x close
33. ( 12 c 3 + 11 c 2 − 15 c + 8 ) ÷ ( − 4 + 3 c ) open 12 , c cubed , plus 11 , c squared , minus 15 c plus 8 close divides open negative 4 plus 3 c close
34. ( 7 b + 16 b 3 ) ÷ ( − 1 + 8 b ) open 7 b plus 16 , b cubed , close divides open negative 1 plus 8 b close
35. ( 4 y + 9 y 3 − 7 ) ÷ ( − 5 + 3 y ) open 4 y plus 9 , y cubed , minus 7 close divides open negative 5 plus 3 y close

Table of Contents