Cho đa thức
\(M\left( x \right) = - 2{x^4} + 4{x^2} - 5x + {3 \over {10}}\)
Tìm đa thức N(x) sao cho
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\(M\left( x \right) + N\left( x \right) = 7 - 12x + {x^2} - {x^4}\)
\(\eqalign{ & M\left( x \right) + N\left( x \right) = 7 - 12x + {x^2} - {x^4} \cr & N(x) = 7 - 12x + {x^2} - {x^4} - M(x) \cr & N(x) = 7 - 12x + {x^2} - {x^4} - ( - 2{x^4} + 4{x^2} - 5x + {3 \over {10}}) \cr & N(x) = 7 - 12x + {x^2} - {x^4} + 2{x^4} - 4{x^2} + 5x - {3 \over {10}} \cr & N(x) = \left( {7 - {3 \over {10}}} \right) + ( - 12x + 5x) + ({x^2} - 4{x^2}) + ( - {x^4} + 2{x^4}) \cr & N(x) = {{67} \over {10}} - 7x - 3{x^2} + {x^4}. \cr}\)