To factor the given expression [tex]\( 3x^{10} - 48x^2 \)[/tex] by factoring out the greatest common factor, follow these steps:
1. Identify the Greatest Common Factor (GCF):
- Look for the common factors in both terms [tex]\( 3x^{10} \)[/tex] and [tex]\( 48x^2 \)[/tex].
- The coefficient of [tex]\( 3x^{10} \)[/tex] is 3, and the coefficient of [tex]\( 48x^2 \)[/tex] is 48.
- The GCF of the coefficients 3 and 48 is 3.
- The variable part [tex]\( x \)[/tex] has a power of 10 in the first term and a power of 2 in the second term. The lowest power of [tex]\( x \)[/tex] common to both terms is [tex]\( x^2 \)[/tex].
2. Factor out the GCF from each term:
- Factoring out [tex]\( 3x^2 \)[/tex] from [tex]\( 3x^{10} \)[/tex], we get [tex]\( 3x^2 \cdot x^8 \)[/tex].
- Factoring out [tex]\( 3x^2 \)[/tex] from [tex]\( 48x^2 \)[/tex], we get [tex]\( 3x^2 \cdot 16 \)[/tex].
3. Rewrite the expression using the factored terms:
[tex]\[
3x^{10} - 48x^2 = 3x^2 (x^8 - 16)
\][/tex]
So, the expression [tex]\( 3x^{10} - 48x^2 \)[/tex] can be rewritten by factoring out the greatest common factor [tex]\( 3x^2 \)[/tex] as:
[tex]\[
3x^2 (x^8 - 16)
\][/tex]
### Conclusion
Factoring out the greatest common factor from the given expression [tex]\( 3x^{10} - 48x^2 \)[/tex], the factored form is:
[tex]\[
3x^2 (x^8 - 16)
\][/tex]
