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Factor out the greatest common factor.

[tex]3x^3 + 7x^2 + 27x[/tex]

[tex]\boxed{x(3x^2 + 7x + 27)}[/tex]

Sagot :

GinnyAnswer
Sure, let's factor out the greatest common factor from the given polynomial [tex]\( 3x^3 + 7x^2 + 27x \)[/tex]. Here is the step-by-step solution:

1. Identify the terms in the polynomial:
[tex]\[ 3x^3, \quad 7x^2, \quad 27x \][/tex]

2. Determine the greatest common factor (GCF) of the terms:
- Identify the common factors in each term:
- [tex]\( 3x^3 \)[/tex] has factors: [tex]\( 3 \times x \times x \times x \)[/tex]
- [tex]\( 7x^2 \)[/tex] has factors: [tex]\( 7 \times x \times x \)[/tex]
- [tex]\( 27x \)[/tex] has factors: [tex]\( 27 \times x \)[/tex]

- The common factor across all terms is [tex]\( x \)[/tex] since each term has at least one [tex]\(x\)[/tex].

3. Factor out the GCF (which is [tex]\( x \)[/tex]):
[tex]\[ 3x^3 + 7x^2 + 27x = x(3x^2) + x(7x) + x(27) \][/tex]

4. Rewrite the polynomial with the GCF factored out:
[tex]\[ 3x^3 + 7x^2 + 27x = x(3x^2 + 7x + 27) \][/tex]

Thus, the factored form of the polynomial [tex]\( 3x^3 + 7x^2 + 27x \)[/tex] is:
[tex]\[ x(3x^2 + 7x + 27) \][/tex]

So, we have successfully factored out the greatest common factor from the given polynomial.
Hi1315

Answer:

x(3x²+7x+27)  

Step-by-step explanation:

To factor out the greatest common factor (GCF) from the expression  [tex]3x^3 + 7x^2 + 27x[/tex] , follow these steps:

1. Identify the GCF of the terms:

  The terms are  [tex]3x^3 , 7x^2 , \:and \: 27x .[/tex]

  - The coefficients are 3, 7, and 27. The GCF of these coefficients is 1 since 3, 7, and 27 have no common factors other than 1.

  - The variable part involves  x  with the smallest power being  x  (as  x  is present in all terms).

  Therefore, the GCF is  x .

2. Factor out the GCF:

Factor  x  out from each term:

[tex]3x^3 + 7x^2 + 27x = x(3x^2 + 7x + 27)[/tex]

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