How do you factor 3x^3-192?

Question

I thought you would just take out the 3 and make it 3(x^3-64) but then I remembered these are the ones that would be 3(    )(     ) but I cannot get my answer into that form.

Answer 1

3x^3 - 192

 

Factor out the 3:

 

3(x^3 - 64)

 

 

Since x^3 - 64 is a difference of two cubes, 

 

(a^3 - b^3) = (a - b) (a^2 + ab + b^2),

 

and a = x and b = 4:

 

 

 

3(x - 4)(x^2 + 4x + 16)

 

Check:

3(x^3 + 4x^2 + 16x - 4x^2 - 16x - 64)

 

 

Hope this helps.

Jason