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Cho các đa thức
\(\eqalign{ & P\left( x \right) = 3{x^2} – 4x + 1 \cr & Q\left( x \right) = 5{x^3} – 2x – 4 \cr & R\left( x \right) = 2x – 7{x^4} + 3 \cr}\)
Hãy tính P(x) + Q(x) + R(x) và
P(x) – Q(x) – R(x).
\(\eqalign{ & P(x) + Q(x) + R(x) = (3{x^2} – 4x + 1) + (5{x^3} – 2x – 4) + (2x – 7{x^4} + 3) \cr & = 3{x^2} – 4x + 1 + 5{x^3} – 2x – 4 + 2x – 7{x^4} + 3 \cr & = 3{x^2} + ( – 4x – 2x + 2x) + (1 – 4 + 3) + 5{x^3} – 7{x^4} = 3{x^2} – 4x + 5{x^3} – 7{x^4}. \cr & P(x) – Q(x) – R(x) = (3{x^2} – 4x + 1) – (5{x^3} – 2x – 4) – (2x – 7{x^4} + 3) \cr & = 3{x^2} – 4x + 1 – 5{x^3} + 2x + 4 – 2x + 7{x^4} – 3 \cr & = 3{x^2} + ( – 4x + 2x – 2x) + (1 + 4 – 3) – 5{x^3} + 7{x^4} = 3{x^2} – 4x + 2 – 5{x^3} + 7{x^4}. \cr}\)