Question 1: Which expression correctly shows 2x^5−54x^2 factored over the integers using the difference of cubes method?

a. (x−3)(x^2+3x+9)
b. x^2(2x−54)(4x^2+54x+2916)
c. 2x^2(x−3)(x^2+3x+9)
d. The polynomial cannot be factored over the integers using the difference of cubes method.
2(x−54)(x^2−54x+2916)

Question 2: Which of the following expressions are factors of p(x)=4x^6+32x^3?

There may be more than one correct answer. Select all correct answers.

1. 4x^3
2. x+2
3. x+8
4. x^3+4
5. x^2−2x+4
6. x^2+2x+4

Question 1:  Option C, 2x^2(x - 3)(x^2 + 3x + 9)

Question 2:  Options 1, 2, 5

Step-by-step explanation:

Question #3

Step 1:  Factor

2x^5 − 54x^2

2x^2(x^3 - 27)

2x^2(x - 3)(x^2 + 3x + 9)

 Option C, 2x^2(x - 3)(x^2 + 3x + 9)

Question #2

p(x) = 4x^6 + 32x^3

Step 1:  Factor

4x^6 + 32x^3

4x^3(x^3 + 8)

4x^3(x + 2)(x^2 - 2x + 4)

 Options 1, 2, 5

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