Answer :

We start with the expression
[tex]$$21x^7 + 9x^6 + 33x^4.$$[/tex]

Step 1. Find the Greatest Common Factor (GCF) of the Numeric Coefficients

The coefficients are 21, 9, and 33. Their greatest common factor is 3.

Step 2. Find the GCF of the Variable Parts

The variable [tex]$x$[/tex] appears in each term with exponents 7, 6, and 4. The smallest exponent is 4. So, the common variable factor is [tex]$x^4$[/tex].

Step 3. Write the Overall GCF

The overall GCF of the expression is
[tex]$$3x^4.$$[/tex]

Step 4. Factor Out the GCF

Divide each term in the expression by [tex]$3x^4$[/tex]:

- For [tex]$21x^7$[/tex]:
[tex]$$\frac{21x^7}{3x^4} = 7x^{7-4} = 7x^3.$$[/tex]

- For [tex]$9x^6$[/tex]:
[tex]$$\frac{9x^6}{3x^4} = 3x^{6-4} = 3x^2.$$[/tex]

- For [tex]$33x^4$[/tex]:
[tex]$$\frac{33x^4}{3x^4} = 11.$$[/tex]

Thus, after factoring out [tex]$3x^4$[/tex], we are left with:
[tex]$$7x^3 + 3x^2 + 11.$$[/tex]

Step 5. Write the Fully Factored Expression

The final factored form of the expression is:
[tex]$$3x^4\left(7x^3 + 3x^2 + 11\right).$$[/tex]

Thanks for taking the time to read Factor the following expression completely by pulling out the GCF tex 21x 7 9x 6 33x 4 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