Advertisements (Quảng cáo)
Cho các đa thức:
\(f(x) = {x^4} – 3{{\rm{x}}^2} + x – 1\)
\(g(x) = {x^4} – {x^3} + {x^2} + 5\)
Tìm đa thức h(x) sao cho:
a) f(x) + h(x) = g(x)
b) f(x) – h(x) = g(x)
a) f (x) + h (x) = g (x)
Advertisements (Quảng cáo)
\( \Rightarrow h(x) = g(x) – f(x) \)
\(h(x)= \left( {{x^4} – {x^3} + {x^2} + 5} \right) – ({x^4} – 3{{\rm{x}}^2} + x – 1)\)
\(\eqalign{
& h(x) = {x^4} – {x^3} + {x^2} + 5 – {x^4} + 3{{\rm{x}}^2} – x + 1 \cr
& h(x) = – {x^3} + 4{{\rm{x}}^2} – x + 6 \cr} \)
b) f (x) – h (x) = g (x)
\(\eqalign{
& \Rightarrow h(x) = f(x) – g(x) \cr
& \Leftrightarrow h(x) = ({x^4} – 3{{\rm{x}}^2} + x – 1) – ({x^4} – {x^3} + {x^2} + 5) \cr} \)
\(\eqalign{
& \Leftrightarrow h(x) = {x^4} – 3{{\rm{x}}^2} + x – 1 – {x^4} + {x^3} – {x^2} – 5 \cr
& \Leftrightarrow h(x) = {x^3} – 4{x^2} + x – 6 \cr} \)