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Answer :
To factor the expression [tex]\( 60x^3 + 50x^5 \)[/tex] completely, we can follow these steps:
1. Identify the greatest common factor (GCF):
Both terms in the expression have a common factor. Look at the coefficients and the variable parts:
- Coefficients: 60 and 50 have a common factor of 10.
- Variable powers: [tex]\( x^3 \)[/tex] and [tex]\( x^5 \)[/tex] both contain [tex]\( x^3 \)[/tex].
Thus, the greatest common factor of the entire expression is [tex]\( 10x^3 \)[/tex].
2. Factor out the GCF:
Divide each term of the expression by the GCF and factor it out:
[tex]\[
60x^3 + 50x^5 = 10x^3(6) + 10x^3(5x^2)
\][/tex]
Simplifying inside the parentheses gives:
[tex]\[
60x^3 + 50x^5 = 10x^3(6 + 5x^2)
\][/tex]
3. Check for further factoring:
Look inside the parentheses to see if [tex]\( 6 + 5x^2 \)[/tex] can be factored further. Since it is a sum and not a difference of squares or a recognizable pattern that can be factored further, we conclude that it is already in simplest factored form.
Therefore, the completely factored expression is:
[tex]\[
10x^3(5x^2 + 6)
\][/tex]
This is the final, fully factored form of the expression [tex]\( 60x^3 + 50x^5 \)[/tex].
1. Identify the greatest common factor (GCF):
Both terms in the expression have a common factor. Look at the coefficients and the variable parts:
- Coefficients: 60 and 50 have a common factor of 10.
- Variable powers: [tex]\( x^3 \)[/tex] and [tex]\( x^5 \)[/tex] both contain [tex]\( x^3 \)[/tex].
Thus, the greatest common factor of the entire expression is [tex]\( 10x^3 \)[/tex].
2. Factor out the GCF:
Divide each term of the expression by the GCF and factor it out:
[tex]\[
60x^3 + 50x^5 = 10x^3(6) + 10x^3(5x^2)
\][/tex]
Simplifying inside the parentheses gives:
[tex]\[
60x^3 + 50x^5 = 10x^3(6 + 5x^2)
\][/tex]
3. Check for further factoring:
Look inside the parentheses to see if [tex]\( 6 + 5x^2 \)[/tex] can be factored further. Since it is a sum and not a difference of squares or a recognizable pattern that can be factored further, we conclude that it is already in simplest factored form.
Therefore, the completely factored expression is:
[tex]\[
10x^3(5x^2 + 6)
\][/tex]
This is the final, fully factored form of the expression [tex]\( 60x^3 + 50x^5 \)[/tex].
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