Answer :
To factor the expression [tex]\(60x^3 + 50x^5\)[/tex] completely, let's follow these steps:
1. Identify the Greatest Common Factor (GCF):
First, look for a common factor in all the terms. Both terms [tex]\(60x^3\)[/tex] and [tex]\(50x^5\)[/tex] have a common numerical factor, as well as a common variable factor.
- For the coefficients 60 and 50, the greatest common factor is 10.
- For the variable part, both terms have at least [tex]\(x^3\)[/tex] as a factor.
Therefore, the GCF of the expression is [tex]\(10x^3\)[/tex].
2. Factor out the GCF:
Divide each term by the GCF and factor it out of the expression:
[tex]\[
60x^3 + 50x^5 = 10x^3( \frac{60x^3}{10x^3} + \frac{50x^5}{10x^3} )
\][/tex]
Simplifying inside the parentheses:
- [tex]\(\frac{60x^3}{10x^3} = 6\)[/tex]
- [tex]\(\frac{50x^5}{10x^3} = 5x^2\)[/tex]
So, the expression becomes:
[tex]\[
60x^3 + 50x^5 = 10x^3 (6 + 5x^2)
\][/tex]
3. Final Factored Form:
The completely factored form of the expression is:
[tex]\[
\boxed{10x^3(5x^2 + 6)}
\][/tex]
Here, [tex]\(10x^3\)[/tex] is the factor common to both terms initially, and [tex]\(5x^2 + 6\)[/tex] is the remaining expression after factoring out the GCF. This is the complete factorization of the given expression.
1. Identify the Greatest Common Factor (GCF):
First, look for a common factor in all the terms. Both terms [tex]\(60x^3\)[/tex] and [tex]\(50x^5\)[/tex] have a common numerical factor, as well as a common variable factor.
- For the coefficients 60 and 50, the greatest common factor is 10.
- For the variable part, both terms have at least [tex]\(x^3\)[/tex] as a factor.
Therefore, the GCF of the expression is [tex]\(10x^3\)[/tex].
2. Factor out the GCF:
Divide each term by the GCF and factor it out of the expression:
[tex]\[
60x^3 + 50x^5 = 10x^3( \frac{60x^3}{10x^3} + \frac{50x^5}{10x^3} )
\][/tex]
Simplifying inside the parentheses:
- [tex]\(\frac{60x^3}{10x^3} = 6\)[/tex]
- [tex]\(\frac{50x^5}{10x^3} = 5x^2\)[/tex]
So, the expression becomes:
[tex]\[
60x^3 + 50x^5 = 10x^3 (6 + 5x^2)
\][/tex]
3. Final Factored Form:
The completely factored form of the expression is:
[tex]\[
\boxed{10x^3(5x^2 + 6)}
\][/tex]
Here, [tex]\(10x^3\)[/tex] is the factor common to both terms initially, and [tex]\(5x^2 + 6\)[/tex] is the remaining expression after factoring out the GCF. This is the complete factorization of the given expression.
