Thu gọn các đa thức, ta có:
\(\displaystyle f(x) = {x^5} - 3{{\rm{x}}^2} + 7{{\rm{x}}^4} - 9{{\rm{x}}^3}\)\(\displaystyle + {x^2} - {1 \over 4}x \)
\(=x^5+7x^4-9x^3+(-3x^2+x^2)\)\(-\dfrac{1}{4}x\)
\(\displaystyle = {x^5} + 7{{\rm{x}}^4} - 9{{\rm{x}}^3} \)\(\displaystyle - 2{x^2} - {1 \over 4}x\)
\(\displaystyle g(x) = 5{{\rm{x}}^4} - {x^5} + {x^2} - 2{{\rm{x}}^3} \)\(\displaystyle + 3{{\rm{x}}^2} - {1 \over 4} \)
\(\displaystyle g(x) = 5x^4 - {x^5} + (x^2+3x^2) \)\(\displaystyle - 2x^3 - {1 \over 4} \)
\(\displaystyle = - {x^5} + 5{{\rm{x}}^4} - 2{{\rm{x}}^3} \)\(\displaystyle + 4{x^2} - {1 \over 4}\)
Suy ra:
