Respuesta :

MathWiz0001

Step-by-step explanation:

We're going to be factoring:

[tex]12 {x}^{4} + 27 {x}^{3} + 6 {x}^{2} [/tex]

We know that the GCF between 12, 27, and 6 is 3.

We also know that the GCF of x^4, x^3, and x^2 is x^2.

When factoring:

  • Use both of our GCFs, 3 and x^2 (3x^2).
  • Divide our coefficients by the GCF.

[tex]3{x}^{2} (4 {x}^{2} + 9x + 2)[/tex]

We know 3x^2 is the correct option since the polynomial is factored completely.

semsee45

Answer:

[tex]3x^2[/tex]

Step-by-step explanation:

[tex]12x^4 + 27x^3 + 6x^2[/tex]

The coefficients of the variables are 12, 27 and 6.  The greatest common factor (GCF) of these numbers is 3.

[tex]\implies 3(4x^4 +9x^3 + 2x^2)[/tex]

From inspection, the GCF of the variables is [tex]x^2[/tex]

[tex]\implies 3x^2(4x^2+9x + 2)[/tex]

Therefore, the GCF of the terms in the polynomial is [tex]3x^2[/tex]

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