Question

Cho \(C\left(x\right)=x^2-3x+2\)

\(A\left(x\right)=x^4-3x^3+\)ax +b

\(B\left(x\right)=x^2-3x+4\)

Tìm a, b để : a) \(A\left(x\right)⋮B\left(x\right)\)

b) \(A\left(x\right)⋮C\left(x\right)\)

Answer 1

\(\left[{}\begin{matrix}A\left(x\right)=x^4-3x^3+ax+b=x^2\left(x^2-3x+4\right)+\left[\left(a-4\right)x+b\right]=B\left(x\right)+f\left(x\right)\left(a\right)\\A\left(x\right)=x^4-3x^3+ax+b=x^2\left(x^2-3x+2\right)+\left[\left(a-2\right)x+b\right]=C\left(x\right)+g\left(x\right)\left(b\right)\end{matrix}\right.\)

a) \(A\left(x\right)⋮B\left(x\right)\Rightarrow f\left(x\right)=0\Rightarrow\left\{{}\begin{matrix}a=4\\b=0\end{matrix}\right.\)

b)\(A\left(x\right)⋮C\left(x\right)\Rightarrow g\left(x\right)=0\Rightarrow\left\{{}\begin{matrix}a=2\\b=0\end{matrix}\right.\)