f(x)= qi(x)g(x)+r(x)g(x) = q2(x)r(x)+ r2(x)ri(x) = q3(x)r(x)+ r(x)ri-2(x) = q;(x)r.(x)+r(x)rs-3(x) = qs-1(x)rs-2(x) + rs-1(x)rs-2(x) = q,(x)rs-1(x)+r(x)r-1(x) = qs+1(x)r,(x)+ 0区区下81.4最大公因式§1.4 最大公因式 2 1 2 g x q x r x r x ( ) ( ) ( ) ( ) = + 1 3 2 3 r x q x r x r x ( ) ( ) ( ) ( ) = + ……………… ……………… i 2 i i-1 i r x q x r x r x ( ) ( ) ( ) ( ) − = + s 3 s 1 s 2 s 1 r x q x r x r x ( ) ( ) ( ) ( ) − − − − = + s 2 s s 1 s r x q x r x r x ( ) ( ) ( ) ( ) − − = + s 1 s 1 s r x q x r x ( ) ( ) ( ) 0 − + = + 1 1 f x q x g x r x ( ) ( ) ( ) ( ) = +