Question

Cho các đa thức :

                \(f\left(x\right)=x^4-3x^2+x-1\)

                \(g\left(x\right)=x^4-x^3+x^2+5\)

Tìm đa thức \(h\left(x\right)\) sao cho :

a) \(f\left(x\right)+h\left(x\right)=g\left(x\right)\)

b) \(f\left(x\right)-h\left(x\right)=g\left(x\right)\)

Answer 1

a) f (x) + h (x) = g (x)

b) f (x) - h (x) = g (x)

Answer 2

a. Ta có: f(x) + h(x) = g(x)

Suy ra: h(x) = g(x) – f(x) = (x4 – x3 + x2 + 5) – (x4 – 3x2 + x – 1)

= x4 – x3 + x2 + 5 – x4 + 3x2 – x + 1

= -x3 + 4x2 – x + 6

b. Ta có: f(x) – h(x) = g(x)

Suy ra: h(x) = f(x) – g(x) = (x4 – 3x2 + x – 1) – (x4 – x3 + x2 + 5)

= x4 – 3x2 + x – 1 – x4 + x3 – x2 – 5

= x3 – 4x2 + x – 6

Answer 3

f(x) + h (x) = g (x)

(x^4 - 3x^2 + x - 1) + h(x) = x^4 - x^3 + x^2 + 5

h(x) = (x^4 - x^3 + x^2 +5) - (x^4 - 3x^2 + x - 1 )

h(x) = x^4 - x^3 + x^2 + 5 - x^4 + 3x^2 - x +1

h(x) = (x^4 - x^4 ) - x^3 + (x^2 + 3x^2) -x +1

h(x) = -x^3 + 4x^2 -x + 1