Question

Giúp e câu f theo công thức BơZu vs ạ

Answer 1

\(f,f\left(x\right)⋮g\left(x\right)\\ \Leftrightarrow4x^4-13x^3+23x^2+18x-k=\left(x+4\right)\cdot c\left(x\right)\)

Thay \(x=-4\left(\text{Bổ đề Bézout}\right)\)

\(\Leftrightarrow4\cdot\left(-4\right)^4-13\cdot\left(-4\right)^3+23\cdot\left(-4\right)^2+18\left(-4\right)-k=0\\ \Leftrightarrow1024+832+368-72-k=0\\ \Leftrightarrow k=2152\)

Answer 2

\(d,f\left(x\right)⋮g\left(x\right)\\ \Leftrightarrow x^4-8x^3+24x^2+7x+k=\left(x+4\right)\cdot a\left(x\right)\)

Thay \(x=-4\left(\text{Bổ đề Bézout}\right)\)

\(\Leftrightarrow\left(-4\right)^4-8\left(-4\right)^3+24\left(-4\right)^2+7\left(-4\right)+k=0\\ \Leftrightarrow256+512+384-28+k=0\\ \Leftrightarrow k=-1124\)

 

Answer 3

\(e,f\left(x\right)⋮g\left(x\right)\\ \Leftrightarrow3x^4-7x^3+11x^2+x-k=\left(x-4\right)\cdot b\left(x\right)\)

Thay \(x=4\left(\text{Bổ đề Bézout}\right)\) 

\(\Leftrightarrow3\cdot4^4-7\cdot4^3+11\cdot4^2+4-k=0\\ \Leftrightarrow768-448+176+4-k=0\\ \Leftrightarrow k=500\)