Cho hai đa thức a) Tìm b) Tìm nghiệm của đa thức h(x).

* Hướng dẫn giải

a, $f\left(\text{x}\right)=-{\text{2x}}^{\text{2}}-{\text{ 3x}}^{\text{3}}-\text{ 5x }+{\text{ 5x}}^{\text{3}}-\text{ x }+{\text{ x}}^{\text{2}}+\text{ 4x }+\text{ 3 }+{\text{ 4x}}^{\text{2}}$

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

$=2x^3+3x^2-2x+3$

$\text{g}\left(\text{x}\right)={\text{ 2x}}^{\text{2}}-{\text{ x}}^{\text{3}}+\text{ 3x }+{\text{ 3x}}^{\text{3}}+{\text{ x}}^{\text{2}}-\text{ x }-\text{ 9x }+\text{ 2.}$$=\left(-x^3+3x^3\right)+\left(2x^2+x^2\right)+\left(3x-x-9x\right)+2$

$=2x^3+3x^2-7x+2$

Ta có: $\text{h}\left(\text{x}\right)=\text{ f}\left(\text{x}\right)-\text{ g}\left(\text{x}\right)$$=\left(2x^3+3x^2-2x+3\right)-\left(2x^3+3x^2-7x+2\right)$

$=2x^3+3x^2-2x+3-2x^3-3x^2+7x-2$

$=\left(2x^3-2x^3\right)+\left(3x^2-3x^2\right)+\left(-2x+7x\right)+\left(3-2\right)$

$=5x+1$

b)