A ball is thrown vertically upward from the top of a

Question

1. Find the greatest common factor for the following list of terms.

15b³,  35b⁵,  25b⁴

A) 5b⁵

B) 525b¹²

C) 105b³

D) 5b³

2. Find the greatest common factor for the following list of terms.

16(x + y)4, 12(x + y)2

A) 192(x + y)⁶

B) 4(x + y)²

C) 12(x + y)⁴

D) 64(x + y)⁴

3. Find the greatest common factor for the following list of terms.

20x⁶, 70x⁷

A) 10x⁷

B) 5x¹³

C) 10x⁶

D) 140x¹³

4. True or False:   x³ + 4x² –8x–12  can be factored by grouping.

5. Factor by grouping.

3x3 + 8x2 +3x +8

A) (3x + 1)(x² + 8)

B) (x + 8)(3x² + 1)

C) (3x + 8)(x² + 1)

D) 3(x + 8)(x² + 1)

6. Factor completely 81zw² – 49z³.

A) (9zw – 7z²)(9w + 7z)

B) (9w – 7z)(9w + 7z2)

C) (9w – 7z2)(9w + 7z)

D) z(9w – 7z)(9w + 7z)

7. Factor completely x²  -25.

A) (x 5)(x + 5)

B) (x+ 5)(x + 5)

C) x(x -5)

D) 5(x -5)

8. Factor completely p¹² + q⁹.

A) (p⁸ + q³)(p⁴ – p²q³ + q⁶)

B) (p⁴ + q³)(p⁸ – p⁴q³ – q⁶)

C) (p⁴ – q³)(p⁸ + p⁴q³ + q⁶)

D) (p⁴ + q³)(p⁸ – p⁴q³ + q⁶)

9. True or False:  The binomial  s³ + t³ cannot be factored.

10. Factor completely.

27a⁶ + 8b³

A) (3a² – 2b)(9a⁴ + 6a²b + 2b²)

B) (3a² + 2b)(9a⁴ – 6a²b + 4b²)

C) (3a² + 2b)(3a⁴ – 6a²b + 2b²)

D) (a² + b)(27a⁴ – 6a²b + 8b²)

11. Factor completely.

x² –4x –45

A) (x- 5)(x + 9)

B) (x -5)(x –9)

C) (x + 5)(x + 9)

D) (x + 5)(x –9)

12. Factor completely.

14y² + 13y – 12

A) (2y + 3)(7y + 4)

B) (2y + 3)(7y – 4)

C) (2y – 4)(7y – 3)

D) (2y – 3)(7y – 4)

13. Factor completely.

4x² – 12x – 112

A) (4x + 4)(x – 28)

B) (4x + 16)(x – 7)

C) 4(x + 4)(x – 7)

D) 3(x + 16)(x – 7)

14. Factor completely using the trial-and-error method.

18x² + 33xy -  40y²

A) (3x - 5y)(6x + 8y)

B) (6x- 8y)(3x + 5y)

C) (3x - 8y)(6x + 5y)

D) (6x - 5y)(3x + 8y)

15. Factor completely using the trial-and-error method.

–3x2 + 12x – 9

A) –3(x – 1)(x – 3)

B) –(3x – 1)(x – 3)

C) –3(x – 1)(x + 3)

D) 3(x + 1)(x – 3)

16. Factor completely using the trial-and-error method.

4x³ – 12x² –112x

A) 3(x + 16)(x – 7)

B) 4x(x + 4)(x – 7)

C) (4x + 4)(x – 28)

D) 4(x + 4)(x2 – 7x)

20. Find the zeros of the function.

f(x) = 4x2 – 32x + 28

A) {–1, 7}

B) {–7, 4}

C)  {-1/7,7}

D) {1, 7}

21. A ball is thrown vertically upward from the top of a building 500 ft high.  If the ball is thrown with an initial velocity of 64 ft/s, the height of the ball, in feet, above the ground after t seconds is given by

h = –16t² + 64t + 500

After how many seconds will the ball be level with the top of the building again?

A) 8 seconds

B) 4 seconds

C) 2 seconds

D) 1 second

22. If a ball is thrown vertically upward from ground level with an initial velocity of 144 ft/s.  After t s, the height h, in feet, is given by

h = –16t² + 144t

When does the ball hit the ground?

A) 9 seconds

B) 9.5 seconds

C) 10 seconds

D) 144 seconds

23. Factor completely, if possible.

15x3 + 25x2 –10x

A) x(3x + 5)(x – 2)

B) x(x + 2)(5x – 1)

C) 5x(x + 2)(3x – 1)

D) Not factorable

24. Factor completely, if possible.

16x² – 60x –16

A) (4x – 4)(4x + 1)

B) 4(4x – 1)(x + 4)

C) 4(x – 4)(4x + 1)

D) Not factorable

25. Factor completely, if possible.

2x² + x + 1

A) (x – 1)(2x – 1)

B) (x – 1)(2x + 1)

C) (x + 1)(2x + 1)

D) Not factorable