Question

Tìm m để đa thức A(x) =2x^3 + x^2 – 4x + m chia hết cho đa thức P(x) = 2x – 1.

Answer 1

\(A\left(x\right)⋮P\left(x\right)=2x-1\\ \Leftrightarrow A\left(\dfrac{1}{2}\right)=2\cdot\dfrac{1}{8}+\dfrac{1}{4}-4\cdot\dfrac{1}{2}+m=0\\ \Leftrightarrow\dfrac{1}{4}+\dfrac{1}{4}-2+m=0\\ \Leftrightarrow m=\dfrac{3}{2}\)

Answer 2

\(2x^3+x^2-4x+m⋮2x-1\)

\(\Rightarrow2x^3-x^2+2x^2-x-3x+\dfrac{3}{2}+m-\dfrac{3}{2}⋮2x-1\)

hay \(m=\dfrac{3}{2}\)