Question

A(x) = 2x⁵ - 3x³ + 7x - 6x⁴ + 2x³ +2

B(x) = x⁵ - 3x³ + 7x - 6x⁴ + x⁵ + 2x²

^{a) Thu gọn 2 đa thức trên}

^{b) Tính A(x) - B(x) và A(x) + B(x)}

^{c) Tìm đa thức C(x) biết C(x) + 2A(x) = B(x)}

Answer 1

a) Ta có: \(A\left(x\right)=2x^5-3x^3+7x-6x^4+2x^3+2\)

\(=2x^5-6x^4-x^3+7x+2\)

Ta có: \(B\left(x\right)=x^5-3x^3+7x-6x^2+x^5+2x^2\)

\(=2x^5-3x^3-4x^2+7x\)

b) Ta có: \(A\left(x\right)-B\left(x\right)\)

\(=2x^5-6x^4-x^3+7x+2-\left(2x^5-3x^3-4x^2+7x\right)\)

\(=2x^5-6x^4-x^3+7x+2-2x^5+3x^3+4x^2-7x\)

\(=-6x^4+2x^3+4x^2+2\)

Ta có: \(A\left(x\right)+B\left(x\right)\)

\(=2x^5-6x^4-x^3+7x+2+2x^5-3x^3-4x^2+7x\)

\(=4x^5-6x^4-4x^3-4x^2+14x+2\)

c) Ta có: C(x)+2A(x)=B(x)

\(\Leftrightarrow C\left(x\right)=B\left(x\right)-2\cdot A\left(x\right)\)

\(\Leftrightarrow C\left(x\right)=2x^5-3x^3-4x^2+7x-2\cdot\left(2x^5-6x^4-x^3-7x+2\right)\)

\(\Leftrightarrow C\left(x\right)=2x^5-3x^3-4x^2+7x-4x^5+12x^4+2x^3+14x-4\)

\(\Leftrightarrow C\left(x\right)=-2x^5+12x^4-x^3-4x^2+21x-4\)