State which method should be applied as the first step for

Question

1. Multiply.     (3x + 9)²

A)  9x² + 54x + 81    B)  3x² + 27x + 81    C)  9x² + 27x + 81    D)  9x² + 81

2. The diameter of the Milky Way disc is approximately 9 *10²⁰ meters.  How long does it take light, traveling at 10¹⁶ m/year to travel across the diameter of the Milky Way?

A)  9,000 years    B)  900,000 years     C)  900 years    D)  90,000 years

3. Multiply.    (4m – 3n)(4m + 3n)

A)  16m² + 24mn – 9n²    B)  16m² + 9n²    C)  16m² – 24mn + 9n²    D)  16m² – 9n²

4. Simplify.     (a⁴b²)⁴

A)  a4b6    B)  a4b8    C)  a8b6    D)  a16b8

5. Remove the parentheses.     –(3x + 5y)

A)  3x – 5y    B)  –3x + 5y    C)  –3x + y    D)  –3x – 5y

6. Find the value of the polynomial x3 – 4x when x = –2.

A)  2    B)  –2    C)  14    D)  0

7. Give the degree.     7x

A)  7    B)  0    C)  1

8. Multiply.  Write the answer in scientific notation.

(2.4 *10^–5)(4 * 10^–4)

A)  9.6 *10^–10    B)  9.6 * 10^–9    C)  9.6 *10²⁰    D)  4.4 * 10^–11

9. A triangle has sides 2x – 5, 3x + 1, and 4x + 2.  Find the polynomial that represents its perimeter.

A)  9x – 2    B)  (2x – 5)(3x + 1)(4x + 2)    C)  10x – 8    D)  24x – 10

10. Arrange in descending-exponent form and give the degree.

8 – x

A)  –x + 8; 0    B)  x – 8; 1    C)  x – 8; 0    D)  –x + 8; 1

11. Find the value of the polynomial –x² + 10x – 10  when x = –5.

A)  –65    B)  –85    C)  –35    D)  15

12. Factor completely.     6x² + 7x + 2

A) (3x + 1)(2x + 2) C) (3x – 2)(2x – 1)

B) (3x + 2)(2x + 1) D) (6x + 2)(x + 1)

13. Factor.    8m⁴n – 16mn⁴

A)  8m⁴n(1 – 2n³)    B)  8m⁴n⁴(m – 2n)    C)  8mn(m³ – 2n³)    D)  8m⁴n(1 – 16mn⁴)

14. Factor completely.     3(x – 2)2 – 3(x – 2) – 6

A)  3(x – 2)(x – 1)    B)  3(x – 2)(x + 1)    C)  3(x – 4)(x + 1)    D)  3(x – 4)(x – 1)

15. Factor completely.     6x² – xy – 5y²

A) (3x – 5y)(2x + y) C) (3x + 5y)(2x – y)

B) (6x – 5y)(x + y) D) (6x + 5y)(x – y)

16. Rewrite the middle term as the sum of two terms and then factor completely.     

10x² + 19x + 6

A) (5x – 2)(2x – 3) C) (5x + 1)(2x + 6)

B) (10x + 2)(x + 3) D) (5x + 2)(2x + 3)

17. Factor completely.    y3 – 12y2 + 36y

A)  y(y – 9)(y + 4)    B)  y(y – 6)2    C)  y(y + 6)2    D)  y(y + 12)(y – 3)

18. State which method should be applied as the first step for factoring the polynomial.

2a² + 9a + 10

A) Use the ac method (or trial and error). C) Group the terms.

B) Find the GCF. D) Factor the difference of squares.

19. Factor.    18x³ – 36x²

A)  18x2(x – 36)    B)  –18x(x2 – 36x)    C)  –9x2(–2x + 4)    D)  –9x2(–2x – 36)

20. Factor completely.     5a² – 125

A)  (5a – 1)(a – 125)    B)  5a(a – 25)    C)  5(a + 5)(a – 5)    D)  5(a – 5)2

21. Factor completely.    b² – ab – 6a²

A)  (b + 3a)(b – 2a)    B)  (b – 6a)(b + a)    C)  (b + 6a)(b – a)    D)  (b – 3a)(b + 2a)

22. Factor completely.     12x³ – 3xy²

A) 3x(4x – y)(x + y) C) 12x(x – 3y)(x – y)

B) 3x(2x – y)2 D) 3x(2x + y)(2x – y)

23. Factor completely.     6z³ – 27z² + 12z

A) 3z(2z – 1)(z – 4) C) 2z(3z – 1)(z – 4)

B) 6z(z – 1)(z – 12) D) z(6z – 1)(z – 12)

24. State which method should be applied as the first step for factoring the polynomial.

(x + 7y)² – 25

A) Factor the difference of squares. C) Use the ac method (or trial and error).

B) Find the GCF. D) Group the terms.

25. Factor.     3a²(a – b) – 6a(a – b) + 21(a – b)

A) 3(a – b)(a2 – 2a + 7) C) (a – b)(3a2 – 6a + 21)

B) (3a – b)(a2 – 2a + 7) D) 3(a – b)(a2 – 6a + 21)

26. Solve.     x² = –6x

A)  2, 6    B)  0, –6    C)  0, 6    D)  6, –6