See Problem 5.

Choose the correct factored form for each expression.

32. k 2 + 5 k n − 84 n 2 k squared , plus 5 k n minus 84 , n squared
    1. ( k − 7 n ) ( k − 12 n ) open k minus 7 n close open k minus 12 n close
    2. ( k − 7 n ) ( k + 12 n ) open k minus 7 n close open k plus 12 n close
33. p 2 − 8 p q − 33 q 2 p squared , minus 8 p q minus 33 , q squared
    1. ( p + 3 q ) ( p − 11 q ) open p plus 3 q close open p minus 11 q close
    2. ( p − 3 q ) ( p + 11 q ) open p minus 3 q close open p plus 11 q close
34. x 2 − 16 x y + 48 y 2 x squared , minus 16 x y plus 48 , y squared
    1. ( x − 4 y ) ( x + 12 y ) open x minus 4 y close open x plus 12 y close
    2. ( x − 4 y ) ( x − 12 y ) open x minus 4 y close open x minus 12 y close

Factor each expression.

35. r 2 + 19 r s + 90 s 2 r squared , plus 19 r s plus 90 , s squared
36. g 2 − 12 g h + 35 h 2 g squared , minus 12 g h plus 35 , h squared
37. m 2 − 3 m n − 28 n 2 m squared , minus 3 m n minus 28 , n squared
38. x 2 + 3 x y − 18 y 2 x squared , plus 3 x y minus 18 , y squared
39. w 2 − 14 w z + 40 z 2 w squared , minus 14 w z plus 40 , z squared
40. p 2 + 11 p q + 24 q 2 p squared , plus 11 p q plus 24 , q squared

B Apply

41. Writing Suppose you can factor x 2 + b x + c x squared , plus b x plus c  as ( x + p ) ( x + q ) . open x plus p close open x plus q close .

    1. Explain what you know about p and q when c > 0 . c greater than 0 .
    2. Explain what you know about p and q when c < 0 . c less than 0 .

42. Error Analysis Describe and correct the error made in factoring the trinomial.

    

43. Think About a Plan The area of a parallelogram is given by the trinomial x 2 − 14 x + 24 . x squared , minus 14 x plus 24 .  The base of the parallelogram is x − 2 . x minus 2 .  What is an expression for the height of the parallelogram?

    • What is the formula for the area of a parallelogram?
    • How can you tell whether the binomial that represents the height has a positive or negative constant term?
44. Recreation A rectangular skateboard park has an area of x 2 + 15 x + 54 . x squared , plus 15 x plus 54 .  What are the possible dimensions of the park? Use factoring.

Write the standard form of each polynomial modeled below. Then factor each expression.

45. 
46. 

47. Reasoning Let x 2 − 13 x − 30 = ( x + p ) ( x + q ) . x squared , minus 13 x minus 30 equals open x plus p close open x plus q close .

    1. What do you know about the signs of p and q?
    2. Suppose | p | > | q | . vertical line p vertical line greater than vertical line q vertical line .  Which number, p or q, is a negative integer? Explain.

48. Reasoning Let x 2 + 13 x − 30 = ( x + p ) ( x + q ) . x squared , plus 13 x minus 30 equals open x plus p close open x plus q close .

    1. What do you know about the signs of p and q?
    2. Suppose | p | > | q | . vertical line p vertical line greater than vertical line q vertical line .  Which number, p or q, is a negative integer? Explain.

Table of Contents