The height of the marble ht in feet at time t seconds is

Question

Chapter 5

1. Find the prime factorization.

   88

   A)  8.11    B) 2².3.11    C) 2³.11    D) 2.44

2. Find the greatest common factor for the given numbers.

   9, 48

   A)  6    B) 9    C) 1    D) 3

3. Find the greatest common factor of the given terms.

   6wx, 14xy, 10wy

   A)  2wx    B) 1    C) 2wxy    D) 2

4. Factor out the greatest common factor.

   (m - 4)8 + (m - 4)m

A) The polynomial is prime. C) (m - 4)8 + m

B) m² + 4m - 32 D)  (m - 4)(8 + m)

5. Factor out the greatest common factor.

   81s²t² - 63s²t + 54st²

A) -9s²t²(-9st + 7s - 6t)   C)  The polynomial is prime.

B) st(81st - 63s + 54t) D)   -9st(-9st + 7s - 6t)

6. Factor out the opposite of the greatest common factor.

   35y³ - 7y²

   A) -7y²(5y - 1)      B) -7y²(-5y + 7)    C) -7y²(-5y + 1)    D) -y²(35y - 7)

7. Factor.

   16r² - 25

A) The expression is prime.   C) (4r - 5)(4r + 5)

B) (4r - 5)²    D) (16r - 5)(16r + 5)

8. Factor.

   36u² - 12u + 1

   A)  The expression is prime.  B)  (6u - 1)²    C) (6u - 1)(6u + 1)    D)  (6u + 1)²

9. Factor completely.

   8w³x - 800wx

A) The expression is prime.      C)  8wx(w - 10)²

B) 8wx(w - 10)(w + 10)   D)  8wx(w² - 10²)

10. Factor completely.

   b³r³ - 12b²r² + 36br

   A)  br(br - 6)²   B)  r(b³r - 6b²)   C)  br(b²r² - 12br + 36)   D)  br(br - 6)(br + 6)

11. Factor.

   vw - 9w - 2v + 18

A) (v - 9)(w - 2) C)  (v + 9)(w + 2)

B) The expression is prime. D)  (v - 2)(w - 9)

12. Factor.

   qrs - 5q - 6rs + 30

A) (q - 6)(rs - 5)     C) The expression is prime.

B) (q + 6)(rs - 5) D) (q - 5)(rs - 6)

13. Factor.

   n² + 5np + 25p²

A) The polynomial is prime. C) (n + 5p)²

B) (n - 5p)(n + 5p)     D) (n + p)(n + 5)

14. Factor the given polynomial completely. If the polynomial is prime, say so.

   w² - 8w

   A) The polynomial is prime.    B) w(w - 8)    C) w(w² - 8w)    D) (w - 8)(w + 8)

15. Factor the given polynomial completely. If the polynomial is prime, say so.

   x³ + xy + 2x² + 2y

A) The polynomial is prime.   C) (x + 2)(x + y)

B) (x + 2)(x² + y)    D) (x² + 2)(x + y)

16. Factor the given polynomial completely.  If the polynomial is prime, say so.

   5r² + 34r + 45

A) (5r - 9)(r + 5)    C) The polynomial is prime.

B) (5r - 9)(r - 5)     D) (5r + 9)(r + 5)

17. Factor the given polynomial completely.

   6v²w - 48vw + 90w

A) w(6v - 30)(6v - 18)   C) The polynomial is prime.

B) 6w(v - 5)(v - 3) D) 6w(v² - 8v + 15)

18. Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial.

   n³ + 4n² - 9n - 36, n + 3

A) (n + 3)(n² - 7n - 12)    C) (n + 3)(n² + n - 12)

B) (n + 3)(n + 3)(n - 4)    D) (n + 3)(n - 3)(n + 4)

19. Factor.

   125x³ - 27

A) (5x - 3)(25x² - 15x + 9)   C) (5x + 3)(25x² - 15x + 9)

B) (5x + 3)(25x² - 30x + 9)   D) (5x - 3)(25x² + 15x + 9)

20. Factor the given polynomial completely.

   c⁴ + d⁴

A) c²d²(c² - d²)      C) The polynomial is prime.

B) (c - d)²(c + d)²     D) (c - d)(c + d)(c² + d²)

21. Factor the given polynomial completely.

   z⁶ - 8z³ + 7

A) The polynomial is prime.   C) (z³ - 7)(z - 1)(z² + z + 1)

B) (z³ - 7)(z - 1)(z² - z - 1)   D) (z³ + 7)(z + 1)(z² + z + 1)

22. Solve the given equation.

   w² = 8w

   A)  8   B) 64      C) 0, 8 D)  8, -8

23. Solve the given equation.

   v³ - 3v² - 13v + 15 = 0

   A)  -3, 1, 5 B)  3, -1     C)  1, 5     D)  3, 1, -5

24. Solve the equation.

1/5x² - 4/5x -1 =0

   A)  1, 5      B)  -1, -5  C)  -1,5     D)  1,-5

25. Audrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t) = -16t² - 54t + 306. How many seconds elapse before the marble hits the ground?

   A)  6 sec      B) 5 sec C) 3 sec D) 4 sec