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Answer :
Final answer:
To factor out the GCF of the polynomial 35x^8 + 25x^7 + 55x^5, we need to find the common factor in the coefficients and the lowest exponent of x. The GCF is 5x^5, so the factored form is 5x^5(7x^3 + 5x^2 + 11).
Explanation:
To factor out the greatest common factor (GCF) from the given polynomial, we need to find the highest power of x that divides each term. First, let's look for the common factor in the coefficients:
- 35, 25, and 55 do not share a common factor other than 5.
To find the GCF in the exponents of x, we look for the lowest exponent present in all the terms:
- The highest power of x present in each term is x8, so the GCF is x5.
Therefore, the factored form of the polynomial is:
5x5(7x3 + 5x2 + 11)
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