Question : Factor the sum or difference of two cubes. 1) t^3 + 64 : 2163462

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Factor the sum or difference of two cubes.

1) t³ + 64

A) (t - 64)(t + 1)(t - 1)

B) (t - 4)(t² + 4t + 16)

C) (t + 4)(t² + 16)

D) (t + 4)(t² - 4t + 16)

2) x³ - 343

A) (x - 7)(x² + 49)

B) (x + 343)(x + 1)(x - 1)

C) (x + 7)(x² - 7x + 49)

D) (x - 7)(x² + 7x + 49)

3) 64p³ + 1

A) (4p + 1)(16p² - 4p + 1)

B) (4p + 1)(16p² + 4p + 1)

C) (4p + 1)(16p² - 4p - 1)

D) (4p + 1)(16p² + 1)

4) 512p³ - 1

A) (8p - 1)(64p² + 1)

B) (8p + 1)(64p² - 8p + 1)

C) (8p - 1)(64p² + 8p + 1)

D) (512p - 1)(p² + 8p + 1)

5) 4k³ + 108

A) 4(k + 3)(k² - 3k + 9)

B) 4(k - 3)(k² + 3k + 9)

C) 4(k + 12)(k² - 12k + 36)

D) 4(k + 3)(k² + 3k + 9)

6) 3r³ - 192

A) 3(r - 4)(r² + 4r + 16)

B) 3(r - 12)(r² + 12r + 48)

C) 3(r - 4)(r² - 4r + 16)

D) 3(r + 4)(r² - 4r + 16)

7) a³b³ + 27

A) (ab + 3)(a²b² - 9)

B) (ab - 3)(a²b² + 9)

C) (ab + 3)(a²b² - 3ab + 9)

D) (ab - 3)(a²b² + 3ab + 9)

8) 8x³ - y³

A) (2x - y)(4x² + y²)

B) (2x + y)(4x² - 2xy + y²)

C) (2x - y)(4x² + 2xy + y²)

D) (8x - y)(x² + 2xy + y²)

9) 54x⁴ - 250xy³

A) 2x(3x + 5y)(9x² - 15xy + 25y²)

B) 2x(3x - 5y)(9x² - 15xy + 25y²)

C) 2(3x - 5y)(9x² + 15xy + 25y²)

D) 2x(3x - 5y)(9x² + 15xy + 25y²)

10) 243x³ - 1125x⁶

A) 9(3x -5x²)(9x² + 15x³ + 25x⁴)

B) 9x³(3 - 5x)(9 + 15x + 25x²)

C) 9(3x + 5x²)(9x² - 15x³ + 25x⁴)

D) 9x³(3 - 5x)(9 + 25x²)

11) 512 - t³

A) (8 - t)(64 + t²)

B) (8 + t)(64 - t²)

C) (8 + t)(64 - 8t + t²)

D) (8 - t)(64 + 8t + t²)

12) 343 + z³

A) (z + 7)(z² + 49)

B) (z - 343)(z² - 1)

C) (z - 7)(z² + 7z + 49)

D) (z + 7)(z² - 7z + 49)

13) 189s³ + 7

A) 7(3s - 1)(9s² + 3s + 1)

B) 7(3s + 1)(9s² - 3s + 1)

C) 7(3s + 1)(9s² + 3s + 1)

D) 7(3s + 7)(9s² - 21s + 7)

14) 5r³ - 320

A) 5(r - 4)(r² - 4r + 16)

B) 5(r - 4)(r² + 4r + 16)

C) 5(r + 4)(r² - 4r + 16)

D) 5(r - 20)(r² + 20r + 80)

15) 384t³ - 6

A) 6(4t + 1)(16t² - 4t + 1)

B) 6(4t - 1)(16t² - 4t + 1)

C) 6(4t - 1)(16t² + 4t + 1)

D) 6(4t - 6)(16t² + 24t + 6)

16) s³ - 343t³

A) (s + 7t)(s² - 7st + 49t²)

B) (s - 7t)(s² + 7st + 49t²)

C) (s - 7t)(s² + 49t²)

D) (s + 343t)(s + t)(s - t)

17) 64p³ + q³

A) (4p + q)(16p² + 4pq + q²)

B) (4p + q)(16p² - 4pq + q²)

C) (4p + q)(16p² - 4pq - q²)

D) (4p + q)(16p² + q²)

List the elements of the set.

18) If A = {x|x is an even integer} and B = {35, 37, 39, 41}, list the elements of A∩B.

A) {x|x is an even integer}

B) ∅

C) {35, 37, 39, 41}

D) {x|x is an even integer or x = 35 or x = 37 or x = 39 or x = 41}

19) If A = {x|x is an odd integer} and B = {59, 61, 62, 64}, list the elements of A∩B.

A) {59, 61}

B) {x|x is an odd integer or x = 62 or x = 64}

C) {x|x is an odd integer}

D) ∅

20) If A = {51, 52, 53, 56} and B = {49, 51, 52, 54}, list the elements of A∩B.

A) ∅

B) {49, 53, 54, 56}

C) {49, 51, 52, 53, 54, 56}

D) {51, 52}

21) If A = {x|x is an even integer} and B = {x|x is an odd integer}, list the elements of A∩B.

A) ∅

B) {x|x is an integer}

C) {x|x is an odd integer}

D) {x|x is an even integer}

22) If A = {21, 23, 24, 25, 28} and B = {21, 23, 24, 25}, list the elements of A∩B.

A) ∅

B) {21, 23, 24, 25}

C) {21, 23, 24, 25, 28}

D) {28}

Solve the compound inequality. Graph the solution set and write the solution in interval notation.

23) x ≤ 3 and x ≥ 1

A) (-∞, 1]U[3, ∞)

B) (1, 3)

C) [1, 3]

D) ∅

24) x ≤ 5 and x ≤ 3

A) (-∞, 3]

B) (-∞, 3]U[5, ∞)

C) [3, ∞)

D) [3, 5]

25) x ≤ -2 and x ≥ 5

A) ∅

B) (-2, 5)

C) (-∞, ∞)

D) [-2, 5]