Question

What is the completely factored form of this polynomial? 18x^3 – 120x^2 – 42x

Answer 1

The completely factored form is 6x(3x+1)(x-7)

Answer 2

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