Answer :
To factor the expression [tex]\(60x^3 + 50x^5\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
Both terms in the expression have numerical coefficients and powers of [tex]\(x\)[/tex]. The numerical coefficients are 60 and 50. The greatest common factor of 60 and 50 is 10. Additionally, both terms have a common variable factor of [tex]\(x^3\)[/tex].
2. Factor out the GCF:
The GCF for the expression [tex]\(60x^3 + 50x^5\)[/tex] is [tex]\(10x^3\)[/tex]. We can factor this out from the expression:
[tex]\[
60x^3 + 50x^5 = 10x^3(6) + 10x^3(5x^2)
\][/tex]
3. Rewrite the expression using the factored form:
Now that you've factored out [tex]\(10x^3\)[/tex], the expression inside the parentheses becomes:
[tex]\[
10x^3(6 + 5x^2)
\][/tex]
4. Final Factored Form:
So, the completely factored form of the expression [tex]\(60x^3 + 50x^5\)[/tex] is:
[tex]\[
10x^3(5x^2 + 6)
\][/tex]
This is your factored expression. The steps we've gone through have broken down the process of factoring the original polynomial by finding and extracting the GCF, leaving us with a simpler expression inside the parentheses.
1. Identify the Greatest Common Factor (GCF):
Both terms in the expression have numerical coefficients and powers of [tex]\(x\)[/tex]. The numerical coefficients are 60 and 50. The greatest common factor of 60 and 50 is 10. Additionally, both terms have a common variable factor of [tex]\(x^3\)[/tex].
2. Factor out the GCF:
The GCF for the expression [tex]\(60x^3 + 50x^5\)[/tex] is [tex]\(10x^3\)[/tex]. We can factor this out from the expression:
[tex]\[
60x^3 + 50x^5 = 10x^3(6) + 10x^3(5x^2)
\][/tex]
3. Rewrite the expression using the factored form:
Now that you've factored out [tex]\(10x^3\)[/tex], the expression inside the parentheses becomes:
[tex]\[
10x^3(6 + 5x^2)
\][/tex]
4. Final Factored Form:
So, the completely factored form of the expression [tex]\(60x^3 + 50x^5\)[/tex] is:
[tex]\[
10x^3(5x^2 + 6)
\][/tex]
This is your factored expression. The steps we've gone through have broken down the process of factoring the original polynomial by finding and extracting the GCF, leaving us with a simpler expression inside the parentheses.
