Answer:
A) x +2
Step-by-step explanation:
Factorizing the expression:
Prime factorize each term and find the GCF.
6x³ = 2 * 3 *x³
12x² = 2 * 2 * 3 * x² = 2² * x²
48x = 2* 2 * 2 * 2 * 3 * x
GCF = 2 * 3 * x = 6x
Take out '6x' from each term,
6x³ - 12x² - 48x = 6x * (x² - 2x - 8)
Now, again factorize the expression using the splitting the middle term method.
x² - 2x - 8
Sum = - 2
Product = -8
Factors are: (-4); 2
When we multiply the factors, we get -4 *2 = -8 and when we subtract, we get (-4) +2 = -2
Rewrite the middle term using the factors,
x² - 4x + 2x - 8 = x*(x - 4) + 2(x -4)
= (x - 4) (x + 2)
6x³ - 12x² - 48x = 6x (x - 4)(x + 2)
x + 2 is a factor.
Answer:
(x + 4) is a factor
Step-by-step explanation:
6x^3 + 12x^2 - 48x
= 6x(x^2 + 2x - 8)
= 6x(x + 4)(x - 2)