1. 2x2+y2+3xy+4x+3y+22. 已知x4+x3+x2+2=(x2+mx+1)(x2+nx+2),那么m+n的值为多少?(要有具体过程)
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![1. 2x2+y2+3xy+4x+3y+22. 已知x4+x3+x2+2=(x2+mx+1)(x2+nx+2),那么m+n的值为多少?(要有具体过程)](/uploads/image/z/1170074-2-4.jpg?t=1.%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B+2x2%2By2%2B3xy%2B4x%2B3y%2B22.%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B%26%23160%3B+%E5%B7%B2%E7%9F%A5x4%2Bx3%2Bx2%2B2%3D%28x2%2Bmx%2B1%29%28x2%2Bnx%2B2%29%2C%E9%82%A3%E4%B9%88m%2Bn%E7%9A%84%E5%80%BC%E4%B8%BA%E5%A4%9A%E5%B0%91%3F%EF%BC%88%E8%A6%81%E6%9C%89%E5%85%B7%E4%BD%93%E8%BF%87%E7%A8%8B%EF%BC%89%26%23160%3B)
1. 2x2+y2+3xy+4x+3y+22. 已知x4+x3+x2+2=(x2+mx+1)(x2+nx+2),那么m+n的值为多少?(要有具体过程)
1. 2x2+y2+3xy+4x+3y+2
2. 已知x4+x3+x2+2=(x2+mx+1)(x2+nx+2),那么m+n的值为多少?(要有具体过程)
1. 2x2+y2+3xy+4x+3y+22. 已知x4+x3+x2+2=(x2+mx+1)(x2+nx+2),那么m+n的值为多少?(要有具体过程)
1.2x2+y2+3xy+4x+3y+2
2x^2+y^2+3xy+4x+3y+2
=(2x^2+2xy+2x)+(y^2+xy+y)+(2x+2y+2)
=2x(x+y+1)+y(x+y+1)+2(x+y+1)
=(2x+y+2)(x+y+1)
2.已知x4+x3+x2+2=(x2+mx+1)(x2+nx+2),那么m+n的值为多少?
x^4+x^3+2=(x^2+mx+1)(x^2+nx+2)
(x^2+mx+1)(x^2+nx+2)=x^4+nx^3+2x^2+mx^3+mnx^2+2mx+x^2+nx+2
=x^4+(n+m)x^3+(3+mn)x^2+(2m+n)x+2
根据题意:m+n为x^3的系数,所以:m+n=1
1.2x^2+y^2+3xy+4x+3y+2
=(2x+y)(x+y)+4x+3y+2
=(2x+y+2)(x+y+1)
2.x4+x3+x2+2=(x2+mx+1)(x2+nx+2)
展开后x^3项的系数为(m+n)
对照系数可知m+n=1
2x^2+y^2+3xy+4x+3y+2
=(2x+y)(x+y)+4x+3y+2
=(2x+y+2)(x+y+1)
x^4+x^3+x^2+2=(x^2+mx+1)(x^2+nx+2)
n+m=1