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: Factor out the GCF

Identify GCF of coefficients and variable. GCF of 18, 120, 42 is 6; GCF of $x^3, x^2, x$ is $x$.
$18x^3 - 120x^2 - 42x = 6x(3x^2 - 20x - 7)$

Step2: Factor quadratic trinomial

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

Step3: Combine all factors

Combine GCF and factored quadratic.
$6x(3x+1)(x-7)$

Answer:

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