Question

3 cho đa thức A(x)=2x⁴-3x³+1/2-4x.tìm đa thức B(x) và đa thức C(x).sao cho

a) A(x)+B(x)=4x⁵-2x²-1

b) A(x)-C(x)=2x³

Answer 1

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

\(\Rightarrow2x^4-3x^3-4x+\dfrac{1}{2}+B\left(x\right)=4x^5-2x^2-1\)

\(\Rightarrow B\left(x\right)=4x^5-2x^2-1-2x^4+3x^3+4x-\dfrac{1}{2}\)

\(\Rightarrow B\left(x\right)=4x^5-2x^4+3x^3-2x^2+4x-\dfrac{3}{2}\)

b) \(A\left(x\right)-C\left(x\right)=2x^3\)

\(\Rightarrow2x^4-3x^3-4x+\dfrac{1}{2}-C\left(x\right)=2x^3\)

\(\Rightarrow C\left(x\right)=2x^4-3x^3-4x+\dfrac{1}{2}-2x^3\)

\(\Rightarrow C\left(x\right)=2x^4-3x^3-2x^3-4x+\dfrac{1}{2}\)

\(\Rightarrow C\left(x\right)=2x^4-5x^3-4x+\dfrac{1}{2}\)

Answer 2

a) B(x) = 4x⁵ -2x² -1 - A(x) = 4x⁵ -2x² -1 -2x⁴ +3x³+4x -1/2

B(x) = 4x⁵ -2x⁴ +3x³-2x² +4x - 1/2

b) tt