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Which of the following represents the factorization of the trinomial below?[tex] - 3 {x}^{3} - 18 {x}^{2} - 24x[/tex]Using these four as possible awnsers A. -3x(x-2)(x-4)B. -3x(x+2)(x+4)C. -3(x²-2)(x-4)D. -3(x²+2)(x+4)

Respuesta :

Hello!

We have the equation below:

[tex]-3x^3-18x^2-24x[/tex]

First of all, note that in all terms we have multiples of -3x. So, let's put it in evidence:

[tex]-3x\cdot(x^2+6x+8)[/tex]

Now, let's rewrite 6x as 4x+2x:

[tex]-3x\cdot(x^2+4x+2x+8)[/tex]

Note that we can put x in evidence because of the first and second terms, and 2 in evidence because of the third and fourth terms. Look:

[tex]-3x\cdot(x^\cdot(x+4)+2(x+4))[/tex]

As we have (x+4) twice, let's put it in evidence too:

[tex]-3x\cdot(x+4)\cdot(x+2)[/tex]

Answer:

Alternative B. -3x(x+2)(x+4)

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