Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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]

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.