求下列多项式的有理根:1.2.3.将该式:化成这种形式
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![求下列多项式的有理根:1.2.3.将该式:化成这种形式](/uploads/image/z/2761658-26-8.jpg?t=%E6%B1%82%E4%B8%8B%E5%88%97%E5%A4%9A%E9%A1%B9%E5%BC%8F%E7%9A%84%E6%9C%89%E7%90%86%E6%A0%B9%EF%BC%9A1.2.3.%E5%B0%86%E8%AF%A5%E5%BC%8F%EF%BC%9A%E5%8C%96%E6%88%90%E8%BF%99%E7%A7%8D%E5%BD%A2%E5%BC%8F)
求下列多项式的有理根:1.2.3.将该式:化成这种形式
求下列多项式的有理根:
1.
2.
3.将该式:
化成这种形式
求下列多项式的有理根:1.2.3.将该式:化成这种形式
(1)
=(x^3-18x)+(x^2-18)
=x(x^2-18)+(x^2-18)
=(x+1)(x^2-18)
(2)
=t^4+t^3-3t^3-3t^2+2t^2+2t-6t-6
=t^3(t+1)-3t^2(t+1)+2t(t+1)-6(t+1)
=(t+1)(t^3-3t^2+2t-6)
=(t+1)[t^2(t-3)+...
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(1)
=(x^3-18x)+(x^2-18)
=x(x^2-18)+(x^2-18)
=(x+1)(x^2-18)
(2)
=t^4+t^3-3t^3-3t^2+2t^2+2t-6t-6
=t^3(t+1)-3t^2(t+1)+2t(t+1)-6(t+1)
=(t+1)(t^3-3t^2+2t-6)
=(t+1)[t^2(t-3)+2(t-3)]
=(t+1)(t-3)(t^2+2)
(3)
=x^5-x^4-x^4+x^3+x^3-x^2+x^2-x-2x+2
=x^4(x-1)-x^3(x-1)+x^2(x-1)+x(x-1)-2(x-1)
=(x-1)(x^4-x^3+x^2+x-2)
=(x-1)[x^3(x-1)+(x-1)(x+2)]
=(x-1)^2(x^3+x+2)
=(x-1)^2[x^3+x^2-x^2-x+2x+2]
=(x-1)^2[x^2(x+1)-x(x+1)+2(x+1)]
=(x+1)(x^2-x+2)(x-1)^2
收起
x³+x²-18x-18
=x²(x+1)-18(x+1)
=(x+1)(x²-18)
x1=-1
t^4-2t^3-t^2-4t-6
=t^4+t^3-3t^3-3t^2+2t^2-6t-6
=t^3(t+1)-3t^2(t+1)+2t(t+1)-6(t+1)
=(t+1)(t^3-3t^2+2t-6)
=(t+1)[t^2(t-3)+2(t-3)]
=(t+1)(t-3)(t^2+2)
t1=-1
t2=3