Answer :
The GCF of [tex]91x^10[/tex]and [tex]39x^5[/tex] is[tex]13x^5[/tex]. Dividing each term by the GCF, the factored form of the expression is[tex]13x^5(7x^5+3).[/tex]
Finding the greatest common factor (GCF) is important in factoring mathematical expressions. In the given expression 91x10+39x5, the GCF is the highest power of any common factor occurring in all terms.
In this case, each term in the expression has 'x' in common. Let's identify the powers of 'x' in each term: x10 and x5. The smaller power is our GCF in terms of variable 'x'. Hence, x5 is the GCF in this case.
Next, we look at the coefficients, which are 91 and 39. The greatest integer that divides both 91 and 39 is 13. Therefore, the GCF of the coefficients is 13.
So, the total GCF for the expression is 13x5. We divide each term in the expression by our GCF to obtain the factored form. Hence, the expression 91x10+39x5 in factored form becomes 7x5x5 + 3x5 = 13x5(7x5+3).
Learn more about the topic of factored here:
https://brainly.com/question/34290719
#SPJ11
