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.