Practice and Problem-Solving Exercises

A Practice Complete.

See Problems 1 and 2.

10. k 2 + 5 k + 6 = ( k + 2 ) ( k +   ) k squared , plus 5 k plus 6 equals open k plus 2 close open k plus begin box , , end box close
11. x 2 − 7 x + 10 = ( x − 5 ) ( x −   ) x squared , minus 7 x plus 10 equals open x minus 5 close open x minus begin box , , end box close
12. t 2 − 10 t + 24 = ( t − 4 ) ( t −   ) t squared , minus 10 t plus 24 equals open t minus 4 close open t minus begin box , , end box close
13. v 2 + 12 v + 20 = ( v + 10 ) ( v +   ) v squared , plus 12 v plus 20 equals open v plus 10 close open v plus begin box , , end box close

Factor each expression. Check your answer.

14. y 2 + 6 y + 5 y squared , plus 6 y plus 5
15. t 2 + 10 t + 16 t squared , plus 10 t plus 16
16. x 2 + 15 x + 56 x squared , plus 15 x plus 56
17. n 2 − 15 n + 56 n squared , minus 15 n plus 56
18. r 2 − 11 r + 24 r squared , minus 11 r plus 24
19. q 2 − 8 q + 12 q squared , minus 8 q plus 12

See Problem 3.

Complete.

20. q 2 + 3 q − 54 = ( q − 6 ) ( q +   ) q squared , plus 3 q minus 54 equals open q minus 6 close open q plus begin box , , end box close
21. z 2 − 2 z − 48 = ( z − 8 ) ( z +   ) z squared , minus 2 z minus 48 equals open z minus 8 close open z plus begin box , , end box close
22. n 2 − 5 n − 50 = ( n + 5 ) ( n −   ) n squared , minus 5 n minus 50 equals open n plus 5 close open n minus begin box , , end box close
23. y 2 + 8 y − 9 = ( y + 9 ) ( y −   ) y squared , plus 8 y minus 9 equals open y plus 9 close open y minus begin box , , end box close

Factor each expression. Check your answer.

24. r 2 + 6 r − 27 r squared , plus 6 r minus 27
25. w 2 − 7 w − 8 w squared , minus 7 w minus 8
26. z 2 + 2 z − 8 z squared , plus 2 z minus 8
27. x 2 + 5 x − 6 x squared , plus 5 x minus 6
28. v 2 + 5 v − 36 v squared , plus 5 v minus 36
29. n 2 − 3 n − 10 n squared , minus 3 n minus 10

See Problem 4.

30. Carpentry The area of a rectangular desk is given by the trinomial d 2 − 7 d − 18 . d squared , minus 7 d minus 18 .  What are the possible dimensions of the desk? Use factoring.

31. Design The area of a rectangular rug is given by the trinomial r 2 − 3 r − 4 . r squared , minus 3 r minus 4 .  What are the possible dimensions of the rug? Use factoring.

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