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Answer :
The greatest common factor (GCF) of 110x^4, 70x^7, and 60x^9 is 10x^4.
To find the greatest common factor (GCF) of the expressions 110x^4, 70x^7, and 60x^9, you need to factor out the highest power of x that is common to all terms and the largest number that divides all the coefficients.
For the coefficients 110, 70, and 60, the GCF is 10.For the variables, we look for the smallest exponent of x present in all terms, which is x^4.Therefore, the GCF of 110x^4, 70x^7, and 60x^9 is 10x^4.
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Final answer:
The greatest common factor of
[tex]110x^4[/tex]7, and 60x^9 is 10x^4, found by identifying the GCF of the numerical coefficients (which is 10) and taking the lowest exponent for x, which is 4.
Explanation:
To find the greatest common factor (GCF) of the expressions 110x^4, 70x^7, and 60x^9, we will first factor out the numerical coefficients and then the variables separately.
The numerical coefficients of the given expressions are 110, 70, and 60. To find the GCF of these numbers, we can list their factors:
- 110: 1, 2, 5, 10, 11, 22, 55, 110
- 70: 1, 2, 5, 7, 10, 14, 35, 70
- 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors are 1, 2, 5, and 10. The greatest of these is 10.
Next, we look at the variable part. Since all expressions are powers of x, we take the lowest exponent of x, which is 4. So, x^4 is the greatest common factor of the variable part.
Therefore, the greatest common factor of 110x^4, 70x^7, and 60x^9 is 10x^4.
