97. Reasoning Explain how to factor 4 x 4 + 24 x 3 + 32 x 2 . 4 x to the fourth , plus , 24 x cubed , plus 32 , x squared , .

Factor each expression completely.

98. x 4 − y 4 x to the fourth , minus , y to the fourth
99. 16 x 4 − 625 y 4 16 x to the fourth , minus . 625 y to the fourth
100. 243 a 5 − 3 a 243 eh to the fifth . minus 3 eh
101. When the expression x 2 + b x − 24 x squared , plus b x minus 24 is factored completely, the difference of the factors is 11. Find both factors if it is known that b is negative.
102. Prove that n 3 − n n cubed , minus n  is divisible by 3 for all positive integer values of n. (Hint: Factor the expression completely.)

Standardized Test Prep

SAT/ACT

103. How can you write ( m − 5 ) ( m + 4 ) + 8 open m minus 5 close open m plus 4 close plus 8  as a product of two binomials?
     1. ( m − 1 ) ( m + 8 ) open m minus 1 close open m plus 8 close
     2. ( m − 4 ) ( m + 3 ) open m minus 4 close open m plus 3 close
     3. ( m + 8 ) ( m + 8 ) open m plus 8 close open m plus 8 close
     4. ( m − 5 ) ( 8 m + 32 ) open m minus 5 close open 8 m plus 32 close
104. The graph of a quadratic function has vertex (7, 6). What is the axis of symmetry?
     6. x = 6 x equals 6
     7. y = 6 y equals 6
     8. x = 7 x equals 7
     9. y = 7 y equals 7

     Extended Response

105. Suppose you hit a baseball and its flight takes a parabolic path. The height of the ball at certain times appears in the table below.

     Time (s)	0.5	0.75	1	1.25
     Height (ft)	10	10.5	9	5.5

     1. Find a quadratic model for the ball's height as a function of time.
     2. Write the quadratic function in factored form.

Mixed Review

See Lesson 4-3.

106. Find a quadratic model for the values in the table.

     x	0	5	10	15	20
     y	17	39	54	61	61

     See Lesson 3-6.

107. Coins The combined mass of a penny, a nickel, and a dime is 9.8 g. Ten nickels and three pennies have the same mass as 25 dimes. Fifty dimes have the same mass as 18 nickels and 10 pennies. Write and solve a system of equations to find the mass of each type of coin.

Get Ready! To prepare for Lesson 4-5, do Exercises 108–110.

See Lesson 4-2.

Graph each function.

108. y = x 2 − 2 x − 5 y equals , x squared , minus 2 x minus 5
109. y = x 2 − 4 x + 4 y equals , x squared , minus 4 x plus 4
110. y = − x 2 − 3 x + 8 y equals negative , x squared , minus 3 x plus 8

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