Coprime polynomials
= Coprime polynomials
{title2=$\gcd(f,g)=1$}
= Coprimality of polynomials
{synonym}
Two <polynomials> over a <field> are coprime if their only common factors are nonzero constants. Equivalently, their <greatest common divisor> is a <unit> in the <polynomial ring>. In one variable this is equivalent to a <Bezout identity> $Af+Bg=1$ with polynomial coefficients. Independent members of a pencil spanned by <coprime polynomials> are themselves coprime.