已知:f(x)=(-3x)^2,f(x)*g(x)=36x^4-4x^3+9x^2,求g(x)的表达式

问题描述:

已知:f(x)=(-3x)^2,f(x)*g(x)=36x^4-4x^3+9x^2,求g(x)的表达式

由已知得f(x)=9x²
因为f(x)*g(x)=36x^4-4x^3+9x^2
所以g(x)=(36x^4-4x³+9x²)/f(x)=(36x^4-4x³+9x²)/9x²
=4x²-4x/9+1

f(x)=(-3x)^2,f(x)*g(x)=36x^4-4x^3+9x^2,
36x^4-4x^3+9x^2=9x^2(4x^2-4/9x+1)
g(x)=(4x^2-4/9x+1)

即f(x)=9x²
所以g(x)=(36x^4-4x³+9x²)/9x²
=4x²-4x/9+1

g(x)= f(x)*g(x)/f(x)
= (36x^4-4x^3+9x^2)/(-3x)^2
=4x^2-4x/9+1