X的四次方,加X的三次方,加四分之九X的平方.加X,加一,因式分解
问题描述：
X的四次方,加X的三次方,加四分之九X的平方.加X,加一,因式分解
答
x^4+x^3+(9/4)x^2+x+1=x^4+(1/2)x^3+x^2+(1/2)x^3+(1/4)x^2+(1/2)x+x^2+(1/2)x+1=x^2(x^2+(1/2)x+1)+(1/2)x(x^2+(1/2)x+1)+(x^2+(1/2)x+1)=(x^2+(1/2)x+1)(x^2+(1/2)x+1)=(x^2+(1/2)x+1)^2