Question

question 4 of 10
what is the factorization of the trinomial below?
-2x³ - 10x² - 12x

a. -2x(x + 3)(x + 2)
b. 2x(x² + 3)(x + 2)
c. -2x(x + 3)(x - 2)
d. -2x(x - 3)(x + 2)

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(-2x^3\), \(-10x^2\), and \(-12x\). The GCF of the coefficients \(-2\), \(-10\), \(-12\) is \(-2\), and the GCF of the variable parts \(x^3\), \(x^2\), \(x\) is \(x\). So, factor out \(-2x\) from the trinomial:
$$-2x^3 - 10x^2 - 12x = -2x(x^2 + 5x + 6)$$

Step2: Factor the quadratic

Now, factor the quadratic \(x^2 + 5x + 6\). We need two numbers that multiply to \(6\) and add up to \(5\). The numbers \(3\) and \(2\) satisfy this (since \(3 \times 2 = 6\) and \(3 + 2 = 5\)). So, we can factor \(x^2 + 5x + 6\) as \((x + 3)(x + 2)\).

Step3: Combine the factors

Substituting the factored form of the quadratic back into the expression, we get:
$$-2x(x + 3)(x + 2)$$

Answer:

A. \(-2x(x + 3)(x + 2)\)