Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Use the Zero-Product Property to solve each equation.

8. ( x − 9 ) ( x − 8 ) = 0 open x minus 9 close open x minus 8 close equals 0
9. ( 4 k + 5 ) ( k + 7 ) = 0 open 4 k plus 5 close open k plus 7 close equals 0
10. n ( n + 2 ) = 0 n open n plus 2 close equals 0
11. − 3 n ( 2 n − 5 ) = 0 negative 3 n open 2 n minus 5 close equals 0
12. ( 7 x + 2 ) ( 5 x − 4 ) = 0 open 7 x plus 2 close open 5 x minus 4 close equals 0
13. ( 4 a − 7 ) ( 3 a + 8 ) = 0 open 4 eh minus 7 close open 3 eh plus 8 close equals 0

See Problems 2 and 3.

Solve by factoring.

14. x 2 + 11 x + 10 = 0 x squared , plus 11 . x plus 10 equals 0
15. g 2 + 4 g − 32 = 0 g squared , plus 4 . g minus 32 equals 0
16. s 2 − 14 s + 45 = 0 s squared , minus 14 . s plus 45 equals 0
17. 2 z 2 − 21 z − 36 = 0 2 z squared , minus 21 z minus 36 equals 0
18. 3 q 2 + q − 14 = 0 3 q squared , plus q minus 14 equals 0
19. 4 m 2 − 27 m − 40 = 0 4 m squared , minus 27 m minus 40 equals 0
20. x 2 + 13 x = − 42 x squared , plus 13 . x equals negative 42
21. p 2 − 4 p = 21 p squared , minus 4 . p equals 21
22. c 2 = 5 c c squared , equals 5 . c
23. 2 w 2 − 11 w = − 12 2 w squared , minus 11 w equals negative 12
24. 3 h 2 + 17 h = − 10 3 h squared , plus 17 h equals negative 10
25. 9 b 2 = 16 9 b squared , equals 16

See Problem 4.

26. Geometry A box shaped like a rectangular prism has a volume of 280  in. 3 . 280 . in. cubed , .  Its dimensions are 4 in. by ( n + 2 ) open n plus 2 close  in. by ( n + 5 ) open n plus 5 close  in. Find n.
27. Knitting You are knitting a blanket. You want the area of the blanket to be 24  ft 2 . 24 , ft squared , .  You want the length of the blanket to be 2 ft longer than its width. What should the dimensions of the blanket be?
28. Construction You are building a rectangular deck. The area of the deck should be 250  ft 2 . 250 , ft squared , .  You want the length of the deck to be 5 ft longer than twice its width. What should the dimensions of the deck be?

B Apply

Use the Zero-Product Property to solve each equation. Write your solutions as a set in roster form.

29. x 2 + 6 x + 8 = 0 x squared , plus 6 . x plus 8 equals 0
30. a 2 + 8 a + 12 = 0 eh squared , plus 8 . eh plus 12 equals 0
31. k 2 + 7 k + 10 = 0 k squared , plus 7 . k plus 10 equals 0

Write each equation in standard form. Then solve.

32. 7 n 2 + 16 n + 15 = 2 n 2 + 3 7 n squared , plus 16 n plus 15 equals , 2 n squared , plus 3
33. 4 q 2 + 3 q = 3 q 2 − 4 q + 18 4 q squared , plus 3 q equals , 3 q squared , minus 4 q plus 18

34. Think About a Plan You have a rectangular koi pond that measures 6 ft by 8 ft. You have enough concrete to cover 72  ft 2 72 , ft squared  for a walkway, as shown in the diagram. What should the width of the walkway be?

    

    • How can you write the outer dimensions of the walkway?

    • How can you represent the total area of the walkway and pond in two ways?

35. Open-Ended Write a quadratic equation in standard form a x 2 + b x + c = 0 eh x squared , plus b x plus c equals 0  such that a, b, and c are integers, but the solutions are rational numbers that are not integers.

36. Error Analysis Describe and correct the error made in solving the equation.

    

37. Reasoning How many solutions does an equation of the form x 2 − k 2 = 0 x squared , minus . k squared , equals , 0  have? Explain.

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