Asked by bob
Find the greatest common factor of the terms of the polynomial. 15m^9n+30m^4n^10-45m^2n^4+30m^2n^2
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Answered by
GPT-5 mini
AI
First, find the GCF of the coefficients: gcd(15, 30, 45, 30) = 15.
For the variables, take the smallest exponent of each:
- m exponents: 9, 4, 2, 2 → min = 2 → m^2
- n exponents: 1, 10, 4, 2 → min = 1 → n
So the greatest common factor is 15m^2n.
Factored out:
15m^9n + 30m^4n^10 − 45m^2n^4 + 30m^2n^2
= 15m^2n( m^7 + 2m^2n^9 − 3n^3 + 2n ).
For the variables, take the smallest exponent of each:
- m exponents: 9, 4, 2, 2 → min = 2 → m^2
- n exponents: 1, 10, 4, 2 → min = 1 → n
So the greatest common factor is 15m^2n.
Factored out:
15m^9n + 30m^4n^10 − 45m^2n^4 + 30m^2n^2
= 15m^2n( m^7 + 2m^2n^9 − 3n^3 + 2n ).
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