Question

tìm A để A chia hết cho B

A= x^4-7x^3+10x^2+(a-1)x + b-a 

B =x^2 -6x +5

 

help me

 

Answer 1

\(A=x^4-7x^3+10x^2+\left(a-1\right)x+b-a\)

\(A=x^4-6x^3+5x^2-x^3+6x^2-5x-x^2+\left(a-1\right)x+b-a\)

\(A=x^2\left(x^2-6x+5\right)-x\left(x^2-6x+5\right)-\left(x^2-\left(a-1\right)x+b-a\right)\)

Ta thấy

\(x^2\left(x^2-6x+5\right)-x\left(x^2-6x+5\right)\) chia hết cho B

\(\Rightarrow-\left(x^2-\left(a-1\right)x+b-a\right)\) phải chia hết cho B

\(\Leftrightarrow\left[{}\begin{matrix}a-1=6\\b-a=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}a=5\\b=0\end{matrix}\right.\)