Answer:
6x(3x + 1)(x - 7) .
Step-by-step explanation:
First look for the greatest common factor of the 3 terms.
It is 6x, so
18x^3 – 120x^2 – 42x
= 6x(3x^2 - 20x - 7)
Now we look to factor the quadratic expression in the parentheses:
Use the 'ac' method:
The first and last coefficients are multiplied
3 * -7 = -21.
We look for 2 numbers whose product is -21 and whose sum is -20:
They are -21 and + 1 , so we write:
6x(3x^2 - 21x + 1x - 7)
= 6x [ (3x(x - 7) + 1(x - 7)] Note that x - 7 is common, so:
= 6x(3x + 1)(x - 7) Answer
