SOLUTION: When finding the greatest common factor of a polynomial, can the factor ever be larger than the smallest coefficient? Can it ever be smaller than the smallest coefficient?
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: When finding the greatest common factor of a polynomial, can the factor ever be larger than the smallest coefficient? Can it ever be smaller than the smallest coefficient?
Log On
Question 375001: When finding the greatest common factor of a polynomial, can the factor ever be larger than the smallest coefficient? Can it ever be smaller than the smallest coefficient? Answer by solver91311(24713) (Show Source):
I'm going to assume that you mean "...can the absolute value of the numerical coefficient ever be larger than the smallest numerical coefficient in the polynomial..."
No. If the coefficient in the potential factor were larger than any of the coefficients in the polynomial, then that coefficient couldn't be a factor of that term of the polynomial.
Yes. Consider a three term polynomial with numerical coefficients of 6, 34, and 22. The GCF of the polynomial would have a numerical coefficient of 2 which is smaller than all of the coefficients.
John
My calculator said it, I believe it, that settles it
