Đáp án:
\(\begin{array}{l}
a.P\left( x \right) = 3{x^5} + {x^4} - 2{x^2} + 2x\\
Q\left( x \right) = - 2{x^5} + 2{x^2} - 2x + 3
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a.P\left( x \right) = x - 2{x^2} + 3{x^5} + {x^4} + x\\
= 3{x^5} + {x^4} - 2{x^2} + 2x\\
Q\left( x \right) = 3 - 2x - 2{x^2} + {x^4} - 2{x^5} - {x^4} + 4{x^2}\\
= - 2{x^5} + 2{x^2} - 2x + 3\\
b.P\left( x \right) + Q\left( x \right) = 3{x^5} + {x^4} - 2{x^2} + 2x - 2{x^5} + 2{x^2} - 2x + 3\\
= {x^5} + {x^4} + 3\\
P\left( x \right) - Q\left( x \right) = 3{x^5} + {x^4} - 2{x^2} + 2x + 2{x^5} - 2{x^2} + 2x - 3\\
= 5{x^5} + {x^4} - 4{x^2} + 4x - 3\\
c.Thay:x = 0\\
\to P\left( 0 \right) = 0\\
Q\left( 0 \right) = 3\\
\to P\left( 0 \right) \ne Q\left( 0 \right)\\
\to dpcm
\end{array}\)