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What is the factored form of this expression?

[tex]\[ -9x^3 - 12x^2 - 4x \][/tex]

A. [tex]\(-x(3x - 2)(3x + 2)\)[/tex]

B. [tex]\(x(3x - 2)(3x + 2)\)[/tex]

C. [tex]\(x(3x - 2)^2\)[/tex]

D. [tex]\(-x(3x + 2)^2\)[/tex]

Sagot :

GinnyAnsweridn
To factor the expression [tex]\(-9x^3 - 12x^2 - 4x\)[/tex], follow these steps:

1. Identify the Greatest Common Factor (GCF):
The GCF of the terms [tex]\(-9x^3\)[/tex], [tex]\(-12x^2\)[/tex], and [tex]\(-4x\)[/tex] is [tex]\(-x\)[/tex].

2. Factor out the GCF:
By factoring [tex]\(-x\)[/tex] from each term, we get:
[tex]\[ -x(9x^2 + 12x + 4) \][/tex]

3. Recognize the quadratic expression:
Now we need to factor the quadratic expression [tex]\(9x^2 + 12x + 4\)[/tex]. The quadratic is of the form [tex]\(ax^2 + bx + c\)[/tex].

4. Factor the quadratic expression:
The quadratic [tex]\(9x^2 + 12x + 4\)[/tex] can be factored into a perfect square trinomial:
[tex]\[ 9x^2 + 12x + 4 = (3x + 2)^2 \][/tex]

5. Combine the factored terms:
Substitute [tex]\( (3x + 2)^2 \)[/tex] back into the expression we factored out earlier:
[tex]\[ -x(9x^2 + 12x + 4) = -x(3x + 2)^2 \][/tex]

Therefore, the fully factored form of the expression [tex]\(-9x^3 - 12x^2 - 4x\)[/tex] is [tex]\(-x(3x + 2)^2\)[/tex].

So, the correct answer is:
D. [tex]\(-x(3x+2)^2\)[/tex]
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