Question

One of the factors of 6x3 − 864x is

A. 4
B. X^2
C. X + 12
D. X - 8

Answer 1

The answer is C. X+12

Answer 2

Consider the expression
`6x^3-864x.` This expression consists of two terms:
`6x^3` and
`-864x.`

These two terms have common factors 6 and x, because:

• 
  `6x^3=6x\cdot x^2;`
• 
  `-864x=6x\cdot (-144).`

Then

`6x^3-864x=6x(x^2-144).`

You know that
`144=12^2.` Use the formula for the difference of squares:

`x^2-144=x^2-12^2=(x-12)(x+12).`

Therefore,

`6x^3-864=6x(x-12)(x+12).`

Answer: correct choice is C.