Middle School

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Which of the trinomials below has [tex]3x^2[/tex] as the greatest common factor (GCF) of its terms?

A. [tex]9x^6 - 18x^4 + 27x^3[/tex]

B. [tex]3x^4 + 9x^2 - 6x[/tex]

C. [tex]9x^4 + 12x^2 - 6x[/tex]

D. [tex]3x^3 + 9x^4 - 6x[/tex]

Answer :

E. None of the above

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Rewritten by : Barada

The trinomial that has [tex]\(3x^2\)[/tex] as the greatest common factor (GCF) of its terms is:[tex]\(3x^4 + 9x^2 - 6x\)[/tex]

The correct option is (B).

To determine the GCF of the trinomials, we need to identify the largest expression that divides each term evenly. For \(3x^4 + 9x^2 - 6x\), the largest expression that divides each term evenly is \(3x\).

Now, let's check the other trinomials:

A.[tex]\(936 - 18x^4 + 27x^3\):[/tex]

The terms here are [tex]\(936\), \(-18x^4\), and \(27x^3\)[/tex]. The common factor for all terms is [tex]\(9x^3\), not \(3x^2\).[/tex]

C. [tex]\(9x^4 + 12x^2 - 6x\):[/tex]

The terms here are \[tex](9x^4\), \(12x^2\), and \(-6x\)[/tex]. The common factor for all terms is [tex]\(3x\), not \(3x^2\).[/tex]

D. [tex]\(3x^3 + 9x^4 - 6x\):[/tex]

The terms here are [tex]\(3x^3\), \(9x^4\), and \(-6x\).[/tex] The common factor for all terms is [tex]\(3x\), not \(3x^2\).[/tex]

Therefore, the correct trinomial with [tex]\(3x^2\)[/tex] as the GCF of its terms is option B.