Question

factor the trinomial completely. if the trinomial contains a greatest common factor (other than 1), factor

(3x^3 - 18x^2 + 24x)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. (3x^3 - 18x^2 + 24x = ) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring trinomials · factoring monomials

Step 1: Factor out the GCF

Identify the greatest common factor (GCF) of the terms in \( 3x^3 - 18x^2 + 24x \):

$$ \text{GCF} = 3x $$

Factor \( 3x \) out of the expression:

$$ 3x(x^2 - 6x + 8) $$

Step 2: Factor the remaining trinomial

Find two numbers that multiply to \( 8 \) and add to \( -6 \):

$$ -2 \text{ and } -4 $$

Write the factored form of the quadratic trinomial \( x^2 - 6x + 8 \):

$$ (x - 2)(x - 4) $$

Combine this with the GCF from Step 1:

$$ 3x(x - 2)(x - 4) $$

Answer:

A. \( 3x^3 - 18x^2 + 24x = 3x(x - 2)(x - 4) \)