Cho đa thức:
A(x)=3x^4-3/4x^3+2x^2-3 ;
B(x)=8x^4+1/5x^3-9x+2/5;
Tính : a, A(x)+ B(x);
b, A(x)-B(x);
c, B(x)-A(x).
Cho đa thức:
A(x)=3x^4-3/4x^3+2x^2-3 ;
B(x)=8x^4+1/5x^3-9x+2/5;
Tính : a, A(x)+ B(x);
b, A(x)-B(x);
c, B(x)-A(x).
Đáp án:
$\begin{array}{l}
a)A\left( x \right) + B\left( x \right)\\
= \left( {3{x^4} – \dfrac{3}{4}{x^3} + 2{x^2} – 3} \right) + \left( {8{x^4} + \dfrac{1}{5}{x^3} – 9x + \dfrac{2}{5}} \right)\\
= 11{x^4} – \dfrac{{11}}{{20}}{x^3} + 2{x^2} – 9x – \dfrac{{13}}{5}\\
b)A\left( x \right) – B\left( x \right)\\
= \left( {3{x^4} – \dfrac{3}{4}{x^3} + 2{x^2} – 3} \right) – \left( {8{x^4} + \dfrac{1}{5}{x^3} – 9x + \dfrac{2}{5}} \right)\\
= – 5{x^4} – \dfrac{{19}}{{20}}{x^3} + 2{x^2} + 9x – \dfrac{{17}}{5}\\
b)B\left( x \right) – A\left( x \right)\\
= – \left( {A\left( x \right) – B\left( x \right)} \right)\\
= – \left( { – 5{x^4} – \dfrac{{19}}{{20}}{x^3} + 2{x^2} + 9x – \dfrac{{17}}{5}} \right)\\
= 5{x^4} + \dfrac{{19}}{{20}}{x^3} – 2{x^2} – 9x + \dfrac{{17}}{5}
\end{array}$