Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Factor the following expression completely by pulling out the GCF:

[tex]\[ 21x^7 + 9x^6 + 33x^4 \][/tex]

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]