Nội dung bài giảng
Tính f (x) + g (x) – h (x) biết:
$$f(x) = {x^5} - 4{{\rm{x}}^3} + {x^2} - 2{\rm{x}} + 1$$
$$g(x) = {x^5} + 2{{\rm{x}}^4} + {x^2} - 5{\rm{x}} + 3$$
$$h(x) = {x^4} - 3{{\rm{x}}^2} + 2{\rm{x}} - 5$$
Giải
f (x) + g (x) – h (x)
\(\eqalign{
& = \left( {{x^5} - 4{{\rm{x}}^3} + {x^2} - 2{\rm{x}} + 1} \right) + \left( {{x^5} + 2{{\rm{x}}^4} + {x^2} - 5{\rm{x}} + 3} \right) + \left( {{x^4} - 3{{\rm{x}}^2} + 2{\rm{x}} - 5} \right) \cr
& = {x^5} - 4{{\rm{x}}^3} + {x^2} - 2{\rm{x}} + 1 + {x^5} + 2{{\rm{x}}^4} + {x^2} - 5{\rm{x}} + 3 + {x^4} - 3{{\rm{x}}^2} + 2{\rm{x}} - 5 \cr
& = (1 + 1){x^5} - (2 + 1){x^4} - 4{{\rm{x}}^3} + (1 + 1 + 3){x^2} - (2 + 5 + 2)x + (1 + 3 + 5) \cr
& = 2{{\rm{x}}^5} - 3{{\rm{x}}^4} - 4{{\rm{x}}^3} + 5{{\rm{x}}^2} - 9{\rm{x}} + 9 \cr} \)