Question

type the correct answer in the box.
what is the completely factored form of this polynomial?
$18x^{3}-120x^{2}-42x$
write the greatest common factor (gcf) first, and write all factors in standard form.

Explanation:

Step1: Find GCF of coefficients

The coefficients are 18, -120, -42. The GCF of 18, 120, 42 is 6. The variable term with the lowest degree is $x$, so overall GCF is $6x$.
Factor out GCF:
$18x^3 - 120x^2 - 42x = 6x(3x^2 - 20x - 7)$

Step2: Factor quadratic trinomial

Factor $3x^2 - 20x - 7$. Find two numbers that multiply to $3\times(-7)=-21$ and add to $-20$. These numbers are $-21$ and $1$.
Split the middle term:
$3x^2 -21x + x -7$
Group and factor:
$3x(x-7) +1(x-7)=(3x+1)(x-7)$

Step3: Combine all factors

Substitute the factored quadratic back into the expression from Step1.

Answer:

$6x(3x+1)(x-7)$