Answer :

Sure, let's factor out the greatest common factor (GCF) from the polynomial [tex]\( 12x^6 + 20x^4 + 8x^3 \)[/tex]. I'll explain the process step-by-step:

1. Identify the GCF of the coefficients (numbers in front of the variables):
- The coefficients are 12, 20, and 8.
- The greatest common factor of 12, 20, and 8 is 4.

2. Identify the GCF of the variables:
- Each term contains the variable [tex]\(x\)[/tex].
- The minimum power of [tex]\(x\)[/tex] present in all terms is [tex]\(x^3\)[/tex].

3. Combine the GCF of the coefficients and the variables:
- The GCF of the polynomial is [tex]\(4x^3\)[/tex].

4. Factor out the GCF from each term in the polynomial:
- Divide each term by [tex]\(4x^3\)[/tex]:
- [tex]\( 12x^6 \div 4x^3 = 3x^3 \)[/tex]
- [tex]\( 20x^4 \div 4x^3 = 5x \)[/tex]
- [tex]\( 8x^3 \div 4x^3 = 2 \)[/tex]

5. Write the factored polynomial:
- Since we factored out [tex]\(4x^3\)[/tex], the polynomial can be rewritten as:
[tex]\[
12x^6 + 20x^4 + 8x^3 = 4x^3 (3x^3 + 5x + 2)
\][/tex]

So, the factored form of the polynomial [tex]\( 12x^6 + 20x^4 + 8x^3 \)[/tex] is:
[tex]\[
4x^3 (3x^3 + 5x + 2)
\][/tex]

Thanks for taking the time to read Factor the GCF out of the polynomial below tex 12x 6 20x 4 8x 3 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada