Factor completely with respect to the integers.
I just need to see if I can simplify or factor the answers I got even further.
1. x^3 + 64
Answer: (x+4)(x^2-4x+16)
Can this simplify any?
2. 8x^3 - 64
Answer 8(x-2)(x^2+2x+4)
3. x^-2x^2+4x-8
Answer: (x^2+4)(x-2)
4. 2x^3 + 3x^2 - 32x - 48
Answer: (x^2-16)(2x+3)
5. 6x^3-18x^2-2x+6
Answer: (6x^2-2)(x-3)
6. x^4 + 12x^3 + 4x^2 + 48x
Answer:(x^3+4x)(x+12)
They look good to me. The first cannot be simplified.
To check if the given answers can be simplified further, you can try factoring the expressions using different methods or techniques.
1. x^3 + 64:
The given answer is (x+4)(x^2-4x+16). This is already factored completely, and it cannot be simplified further.
2. 8x^3 - 64:
The given answer is 8(x-2)(x^2+2x+4). This is already factored completely, and it cannot be simplified further.
3. x^-2x^2+4x-8:
The given answer is (x^2+4)(x-2). This is already factored completely, and it cannot be simplified further.
4. 2x^3 + 3x^2 - 32x - 48:
The given answer is (x^2-16)(2x+3). This is already factored completely, and it cannot be simplified further.
5. 6x^3-18x^2-2x+6:
The given answer is (6x^2-2)(x-3). This is already factored completely, and it cannot be simplified further.
6. x^4 + 12x^3 + 4x^2 + 48x:
The given answer is (x^3+4x)(x+12). This is already factored completely, and it cannot be simplified further.
Therefore, the answers provided for all the expressions are already in their simplified and fully factored form.