Answer :
To factor the expression
[tex]$$60x^3 + 50x^5,$$[/tex]
we begin by identifying the greatest common factor (GCF) of the two terms.
1. Identify the numerical GCF:
The numerical coefficients are 60 and 50. The greatest common divisor (GCD) of 60 and 50 is 10.
2. Identify the common variable factor:
The variable parts are [tex]$x^3$[/tex] and [tex]$x^5$[/tex]. The smallest power of [tex]$x$[/tex] that appears in both terms is [tex]$x^3$[/tex]. Hence, the common factor in terms of [tex]$x$[/tex] is [tex]$x^3$[/tex].
3. Factor out the common factor:
Write each term as a product including the common factor [tex]$10x^3$[/tex]:
[tex]\[
60x^3 = 10x^3 \cdot 6 \quad \text{and} \quad 50x^5 = 10x^3 \cdot 5x^2.
\][/tex]
Therefore, the expression can be written as:
[tex]\[
60x^3 + 50x^5 = 10x^3(6 + 5x^2).
\][/tex]
4. Final factored form:
The completely factored form of the expression is:
[tex]\[
\boxed{10x^3(6+5x^2)}.
\][/tex]
This is the final answer.
[tex]$$60x^3 + 50x^5,$$[/tex]
we begin by identifying the greatest common factor (GCF) of the two terms.
1. Identify the numerical GCF:
The numerical coefficients are 60 and 50. The greatest common divisor (GCD) of 60 and 50 is 10.
2. Identify the common variable factor:
The variable parts are [tex]$x^3$[/tex] and [tex]$x^5$[/tex]. The smallest power of [tex]$x$[/tex] that appears in both terms is [tex]$x^3$[/tex]. Hence, the common factor in terms of [tex]$x$[/tex] is [tex]$x^3$[/tex].
3. Factor out the common factor:
Write each term as a product including the common factor [tex]$10x^3$[/tex]:
[tex]\[
60x^3 = 10x^3 \cdot 6 \quad \text{and} \quad 50x^5 = 10x^3 \cdot 5x^2.
\][/tex]
Therefore, the expression can be written as:
[tex]\[
60x^3 + 50x^5 = 10x^3(6 + 5x^2).
\][/tex]
4. Final factored form:
The completely factored form of the expression is:
[tex]\[
\boxed{10x^3(6+5x^2)}.
\][/tex]
This is the final answer.
