Question

How do you factor `162x^3 + 384`?

Answer 1

`6(3x+4)(9x^2-12x+16)`

Explanation:

`"take out the "color(blue)"common factor"" of 6"`

`rArr6(27x^3+64)to(color(red)(1))`

`27x^3+64" is a "color(blue)"sum of cubes"`

`•color(white)(x)a^3+b^3=(a+b)(a^2-ab+b^2)`

`27x^3=(3x)^3rArra=3x`

`64=(4)^3rArrb=4`

`rArr27x^3+64=(3x+4)(9x^2-12x+16)`

`"returning to "(color(red)(1))`

`rArr162x^3+384=6(3x+4)(9x^2-12x+16)`